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<image>【Problem】As shown in the figure, ∠A = 36°, ∠DBC = 36°, and ∠C = 72°, how many isosceles triangles are there in the figure? _____________ | 3 |
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<image>CBDE is a square. DBF takes on a sector shape. What is the perimeter length of DBF? | 2*π/3 + 4 |
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<image>As shown in the figure, Xiao Ming starts from point $$A$$ on the playground, walks 15 meters in a straight line, then turns left by $$45^{\circ}$$. After walking another 15 meters in a straight line, he turns left again by $$45^{\circ}$$. Continuing in this manner, the total distance he will have walked by the time he returns to the starting point $$A$$ for the first time is ______ meters$$.$$ | 120 |
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<image>As shown in the figure, to measure the distance between the points A and B on opposite sides of the pond, a point C can be selected outside the pond. Connect AC and BC, take the midpoints D and E of AC and BC respectively, and measure DE = 50m. Then the length of AB is ______m. | 100 |
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<image>(2007 Xuhui District Second Mock Exam) As shown in the figure, there are two congruent right-angled triangles with side lengths of 3 and 4. These two right-angled triangles are arranged to form either a triangle or a quadrilateral. Among these shapes, the minimum perimeter is ___.
| 14 |
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<image>As shown in the , in triangle ABC, ∠ABC = 74°, and AD is the altitude of triangle ABC, then ∠BAD = ____ degrees. | 16 |
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<image> As shown in the figure, BD bisects ∠ABC, point E is a point on BA, and EG is parallel to BC, intersecting BD at point F. If ∠1 = 35°, then the measure of ∠ABC is ______. | 70 |
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<image>ABC is an isosceles triangle where the sides AB and BC are identical in length. CBD takes the form of a sector. Square DBEF is inscribed with a circle. What is the total length of the perimeter of circle? | 9*π |
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<image> As shown in the figure, given that ⊙O is the circumcircle of quadrilateral ABCD and ∠BCD = 120°, what is the degree measure of ∠BOD? ______. | 120 |
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<image> As shown in the figure, point E is a point on the side CD of rectangle ABCD. BF is perpendicular to AE at point F. Prove that △ABF is similar to △EAD. | △ABF ∽ △EAD |
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<image>ABC is identified as a sector. CBDE is a square. EDF is defined as a sector. FDG is an isosceles triangle where FD and DG are of equal length. How do you find the perimeter of FDG? | 2*√(2) + 4 |
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<image>The net on the right can be cut out and folded to make a cube. Which face will then be opposite the face marked $\mathbf{x}$ ?
A. a
B. b
C. c
D. d
E. e | E. e |
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<image>As shown in the figure, given that \(\triangle ABC\) is an equilateral triangle, \(BD\) is the median, extend \(BC\) to \(E\) such that \(CE = CD\), connect \(DE\), then \(\angle BDE =\) ______ \(^{\circ}.\) | 120 |
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<image> Using a 120 cm long ribbon to surround the frame (the connection part uses 2 cm), is this ribbon long enough? | Not enough |
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<image>As shown in the , point A is on line MN, and MN is parallel to BC. Prove that: ∠BAC + ∠B + ∠C = 180°. | 180^\circ |
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<image> As shown in the figure, the area of triangle ABE is 48 square decimeters, and BC = CD = DE. Then the area of the shaded part is ____ square decimeters. | 16 |
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<image>DCE is an isosceles triangle, with DC equalling CE. ECF is defined as a sector. In sector ECF, how long is arc EF? | 20*π/3 |
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<image>Calculate the area of the shaded region in the figure below. (Unit: decimeters)
| 63 |
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<image>ABCD is geometrically a square. ADE is in the form of a sector. Square EDFG is inscribed with a circle. In shape EDFG, what is the length of FD? | 3 |
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<image>(Autumn 2008 Zibo Final Exam) As shown in the figure , in triangle ABC, the bisectors of ∠B and ∠C intersect at P, PD is parallel to AB, PE is parallel to AC. If BC = 20 cm, then the perimeter of triangle PDE is ____ cm. | 20 |
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<image>△ABC is positioned in the Cartesian coordinate system as shown in the figure, where each small square has a side length of 1 unit.
(1) Translate △ABC 2 units to the right and draw the translated triangle △A_{1}B_{1}C_{1};
(2) If △ABC is rotated 180° around the point (-1,0), resulting in △A_{2}B_{2}C_{2}, draw the rotated triangle △A_{2}B_{2}C_{2};
(3) Observe the relative positions of △A_{1}B_{1}C_{1} and △A_{2}B_{2}C_{2}:
① The positional relationship between line segments A_{1}C_{1} and A_{2}C_{2} is _______, and the area of quadrilateral A_{1}C_{1}A_{2}C_{2} is ______;
② Are △A_{1}B_{1}C_{1} and △A_{2}B_{2}C_{2} centrally symmetric about a certain point? If so, please write the coordinates of the center of symmetry; if not, explain why. | 8 |
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<image>As shown in the diagram, in $$\triangle ABC$$, $$CD$$ is the altitude from vertex C to side $$AB$$, and $$\dfrac{AD}{CD}= \dfrac{CD}{BD} .$$ Find the measure of $$∠ACB$$. | 90° |
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<image> As shown in the figure, it is a cross-sectional view of a heating pipe. If the direction of the pipe should remain unchanged before and after bending, then the two angles ∠α and ∠β of the pipe should satisfy the relationship ____, and the reason is ____. | ∠α = ∠β |
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<image>(2009 Autumn • Zoucheng City Final Exam) As shown in the , BO bisects ∠CBA, CO bisects ∠ACB, and through point O, EF is drawn parallel to BC. If AB=12 and AC=18, then the perimeter of △AEF is ____. | 30 |
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<image>As shown in the figure, lines \textit{AB} and \textit{CD} intersect at point \textit{O}, \textit{OE} is perpendicular to \textit{AB}, with \textit{O} being the foot of the perpendicular. If ∠\textit{EOD} = 32°, then ∠\textit{AOC} = ________________. | 58 |
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<image>As shown in the figure, point C is on line segment BD. Equilateral triangle BCA and equilateral triangle CDE are constructed on the same side of BD with BC and CD as their side lengths, respectively. Connecting BE and AD intersects AC at M and CE at N, respectively. If CM=x, then CN=______. | x |
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<image>ABC forms a sector. CBD is an isosceles triangle in which CB and BD are equal. DBEF conforms a square. What is the side length FE in the shape DBEF? | 24 |
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<image>As shown in the , it is known that ∠1 + ∠2 = 180°, and ∠DEF = ∠A. Prove that: ∠ACB = ∠DEB. | ∠ACB = ∠DEB |
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<image> As shown in the figure, AB is the diameter of circle O, and points C and D are on circle O. Given that ∠BCD=25°, what is the degree measure of ∠AOD? ____ | 130 |
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<image>As shown in the figure, △ABC is an equilateral triangle, and P is a point inside △ABC. After rotating △ABP counterclockwise about point A, it can coincide with △ACP'. If AP = 3, find the length of PP'. | 3 |
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<image> As shown in the figure, △DEF is scaled down to half of its original size. The procedure is as follows: pick any point P, connect DP and take the midpoint A of DP; then connect EP and FP, and take their midpoints B and C respectively to form △ABC. Which of the following statements are correct?
① △ABC and △DEF are similar figures by homothety (dilation);
② △ABC and △DEF are similar figures;
③ The ratio of the perimeters of △ABC to △DEF is 1:2;
④ The ratio of the areas of △ABC to △DEF is 1:2.
Choose the correct number of statements:
A. 1 statement____
B. 2 statements____
C. 3 statements____
D. 4 statements | 3个 |
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<image>As shown in the figure, given that ∠1 = 34°, then ∠2 = ____.
| 56 |
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<image>As shown in the figure, PA and PB are tangent to circle O at points A and B respectively, and the line FG is tangent to circle O at point E. FG intersects PA at F and intersects PB at G. If PA = 8 cm, then the perimeter of △PFG is (___).
| 16 |
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<image>As shown in the figure, $$E$$ is a point on the extension of side $$DC$$ of parallelogram $$ABCD$$. Draw $$AE$$, intersecting $$BC$$ at point $$F$$. Then, the number of triangles in the figure that are similar to $$\triangle ABF$$ is ________. | 2 |
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<image>As shown in the figure, △ABC ≌ △ADE. If ∠B = 80°, ∠C = 30°, and ∠DAC = 34°, then the measure of ∠EAC is ______. | 36 |
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<image>Given: As shown in the image, ∠1 = ∠2, ∠3 + ∠DCB = 180°, and ∠CME:∠GEM = 4:5. Find the measure of ∠CME.
_____________________ | 80 |
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<image>As shown in the figure, given that $$∠1 = ∠2$$ and $$∠B = 40^{\circ}$$, what is $$∠3=$$ ______ ? | 40^\circ |
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<image>As shown in the figure, in the equilateral $$\triangle ABC$$, it is known that $$BD=CE$$, and $$AD$$ intersects $$BE$$ at point $$P$$. Then $$∠APE$$ is __ degrees.
| 60 |
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<image>ECF is identified as a sector. What is the length of FC in shape ECF? | 63 |
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<image>As shown in the figure, in the plane Cartesian coordinate system, the coordinates of A and B are (2,0) and (0,1) respectively. If the line segment AB is translated to \( A_{1}B_{1} \), then the value of \( a+b \) is ______. | 2 |
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<image>As shown in the figure, during the long jump competition, Xiaoming jumps from point $$A$$ and lands at point $$B$$ in the sandpit. The long jump distance is $$4.2$$ meters. Therefore, the distance from the jump-off point to the landing point is _______________ $$4.2$$ meters. (Fill in with "greater than", "less than", or "equal to") | greater than |
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<image>ABC is an isosceles triangle, having AB and BC of the same length. CBD is an isosceles triangle where CB = BD. DBE is geometrically a sector. What is the arc length DE in the sector DBE? | 14*π |
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<image> As shown in the figure, a ship departs from point \( A \) at sea level and heads \( 40^{\circ} \) south of west for \( 40 \) nautical miles to reach point \( B \). Then from point \( B \), it heads \( 20^{\circ} \) north of west for \( 40 \) nautical miles to reach point \( C \). The distance between points \( A \) and \( C \) is ______ nautical miles. | 40 |
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<image>As shown in the , the clock face of a clock; what is the degree measure of the angle ∠α formed by the minute hand and the hour hand at 8:00? | 120 |
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<image>If the diagonal of the ABCD rectangle is 19, the perimeter of the AEFB rectangle is 52, the AEGHI shape is a combination of a rectangle and an equilateral triangle and the perimeter of the AEGHI shape is 72, compute the length of the AD side of the ABCD rectangle. Round computations to 2 decimal places. | 16.45 |
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<image>Side CD shaping into an equilateral triangle beyond the rectangle. DEF takes the form of a sector. FEG is an isosceles triangle, having FE and EG of the same length. How large are angle EFG and angle FGE in the isosceles triangle FEG? | 30 |
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<image>As shown in the figure, if AB ∥ CD and ∠C = 100°, then ∠A = _____. | 80 |
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<image>The top view of a shell is shown in the figure, with point C dividing the segment AB approximately according to the golden ratio. Given that AB = 10 cm, the length of AC is approximately ___ cm (the result should be accurate to 0.1 cm).
| 6.2 |
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<image>ABCD is geometrically a square. ADEF is geometrically a square. EDG is in the form of a sector. In shape EDG, what is the length of GD? | 24 |
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<image>(Total: 6 points) Given: As shown in the figure, ∠AOB = ∠COD = 90° Find: (1) Are ∠AOC and ∠BOD equal? Please explain why; (2) If ∠BOD = 136°, what is ∠BOC? | Yes |
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<image>As shown in the figure, E, F, G, and H are the midpoints of OA, OB, OC, and OD respectively. Given that the area of the quadrilateral EFGH is 3, then the area of the quadrilateral ABCD is (__)
| 12 |
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<image>In ▱ABCD, ∠A=120°, then ∠1=______ degrees.
| 60° |
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<image>ABCD is geometrically a square. Side EF forming an equilateral triangle. FGH is an isosceles triangle, and the sides FG and GH are of equal length. HGIJ is a square. What is the measurement of the total area of HGIJ? | 100 |
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<image> As shown in the figure, in △ABC, ∠BAC = 5∠ABC, ∠C = 2∠ABC, and BD is perpendicular to AC with D being the foot of the perpendicular. Prove that ∠CBD = 45°. | 45^\circ |
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<image>As shown in the figure, points A, B, and C lie on circle O. If ∠BAC = 20°, then the measure of ∠BOC is ______. | 40 |
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<image> As shown in the figure, points D, E, and F are on the three sides of △ABC, DE∥BC, and ∠A + ∠ADF = 180°.
Prove: ∠B = ∠EDF. | ∠B = ∠EDF |
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<image>As shown in the figure, lines \( AB \) and \( CD \) intersect at point \( O \), and \( OE \) bisects \( ∠BOD \). If \( ∠AOD : ∠DOB = 3 : 2 \), then \( ∠EOB = \) _____. | 36° |
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<image>As shown in the figure, ∠1 = ∠2, CF ⊥ AB, DE ⊥ AB, prove: FG ∥ BC. Proof: ∵ CF ⊥ AB, DE ⊥ AB _(Given) ∴ ∠BED = 90°, ∠BFC = 90° (______________) ∴ ∠BED = ∠BFC (______________) ∴ ED ∥ FC ____ (_________________________) ∴ ∠1 = ∠BCF _ (_________________________) ∵ ∠2 = ∠1 ___(_Given) ∴ ∠2 = ∠BCF _ (_____________) ∴ FG ∥ BC ____ (_________________________)_ | FG ∥ BC |
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<image>Zhang Ming's father used a fence to enclose a rectangular vegetable garden that is 12 meters long and 6 meters wide. If one side is against the wall (as shown in the diagram), what is the minimum length of the fence required? | 24 |
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<image>As shown in the figure, in parallelogram ABCD, it is known that AD = 5 cm and AB = 3 cm. AE bisects ∠BAD and intersects side BC at point E. Find the length of EC (___) | 2 |
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<image>As shown in the figure, the diagonals of the parallelogram ABCD intersect at point O, and AB = 5. The perimeter of triangle OCD is 13. Then the sum of the lengths of the two diagonals of the parallelogram ABCD is ____. | 16 |
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<image> As shown in the figure, △ABC is inscribed in circle O, ∠BAC=120°, AB=AC=4. BD is the diameter of circle O, then BD=____. | 8 |
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<image>ABCD conforms a square. ADE is geometrically a sector. Square EDFG holds an inscribed circle. In shape EDFG, what is the length of FD? | 3 |
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<image> (2011 Autumn • Jiaxing Final Exam) As shown in the figure, it is known that AB ∥ CD, CE bisects ∠ACD and intersects AB at E, and ∠AEC = 28°. Then, ∠A = ____. | 124 |
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<image>As shown in the figure, AC and BD intersect at point O, and AO = DO. Try adding a condition to make △AOB ≌ △DOC. The condition you added is: ___ (Just write one condition).
| OB=OC |
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<image>(2011 Spring • Laizhou City Midterm) As shown in the , quadrilateral ABCD is a square. △ADE, when rotated, can coincide with △ABF. Then, ∠EAF is equal to ____. | 90^\circ |
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<image>As shown in the , it is known that in △ABC, AB=AC, the bisectors of ∠BAC and ∠ACB, AF and CE, intersect at point D, and ∠B=70°, then the measure of ∠ADE is ____ degrees. | 55 |
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<image> As shown in the figure, if a second square ACEF is constructed with the diagonal AC of the square ABCD as its side, and a third square AEGH is constructed with the diagonal AE of the square ACEF as its side, and so on..., given that the area of the square ABCD, S_{1}, is 1, the areas of the subsequent squares constructed in the described manner are S_{2}, S_{3}, ..., S_{n} (where n is a positive integer). Then the area of the 8th square S_{8}=(___ ), and S_{n}=(___ ). | 128 |
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<image>As shown in the figure, in trapezoid ABCD, AB∥CD, AB=4, CD=2. Points E and F are on AD and BC respectively, and EF=3, EF∥AB. Then the area ratio between trapezoid ABFE and trapezoid EFCD is _______.
| 7:5 |
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<image>ABC is an isosceles triangle where AB = BC. CBD is an isosceles triangle, with CB equalling BD. DBEF forms a square. What is the measurement of the total area of DBEF? | 1225 |
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<image>As shown in the figure, the rectangle is composed of $$8$$ small squares with side lengths of $$3cm$$. The area of the shaded part in the figure is ______ $$cm^{2}$$. | 18 |
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<image>ABC is geometrically a sector. CBDE is geometrically a square. How would you calculate the perimeter of CEF? | 35*√(2) + 70 |
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<image>As shown in the figure, place two triangular plates with their right angle vertices coinciding on a table surface. If $$∠AOD=140^{\circ}$$, then $$∠BOC=$$_____ degrees.
| 40 |
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<image>As shown in the , point $$O$$ is the intersection of lines $$AB$$ and $$CD$$, with $$∠AOE=∠COF=90^{\circ}$$. If $$∠EOF=32^{\circ}$$, find the degree measure of $$∠AOD$$. | 148 |
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<image>In the renovation project of National Highway 207 in the Xiangyang section, it is necessary to excavate and build the road along the AC direction, as shown in the figure. To expedite the construction, working from the other side of the small hill simultaneously is required. From point B on AC, take ∠ABD = 140°, BD = 1,000 meters, ∠D = 50°. In order to make the excavation point E on the straight line AC, DE = (____) meters (trigonometric function values provided for reference: sin50° = 0.7660, cos50° = 0.6428, tan50° = 1.192). | 642.8 |
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<image>One day, Xiaofang went to Teacher Jin’s office to play and accidentally knocked over an ink bottle on the desk, causing the problem on the desk to change to: "As shown in the figure, given that AB⊥BC, (conditions that have been obscured by ink and are thus indiscernible), BC=EC, and CA bisects ∠BCD, try to explain why AC=DC."
1. Based on the available information, can you determine the measure of ∠DEC? If yes, write down the solution process; if not, please explain the reason.
2. Please give Xiaofang an idea to make the original problem complete. The condition you added is ____(only list one). | 90^\circ |
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<image>As shown in the figure, in the cyclic quadrilateral ABCD inscribed in circle O, if ∠A = 115°, then ∠BOD is equal to _
| 130 |
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<image> In quadrilateral ABCD, AC = 4 cm, BD = 4.5 cm, E, F, G, and H are the midpoints of sides AB, BC, CD, and DA respectively. The perimeter of quadrilateral EFGH is (___) cm. | 8.5 |
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<image>As shown in the (2013 Autumn • Dongguan City Midterm at the School Level), in triangle ABC, ∠C is 90°, AD bisects ∠CAB, BC is 8cm, BD is 5cm, then DE equals ____ cm. | 3 |
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<image>Given: As shown in the figure, BC is the diameter of the semicircle, O is the center of the circle, D is the midpoint of arc AD, and the diagonals AC and BD of quadrilateral ABCD intersect at point E. Prove: ⊿ABE∽⊿DBC. | △ABE ∽ △DBC |
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<image> A certain university randomly selected the scores of 100 students from the 1000 students participating in this year's independent admission examination, and obtained the sample frequency distribution histogram as shown in the figure. If a score of 60 or above is considered passing, estimate the number of students who pass among these 1000 students. ____ students. | 700 |
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<image>The following math problem translated from Chinese to English, retaining the placeholder, is as follows:
A school conducted a physical education test for all students in the eighth grade (1) class. The test scores are divided into four levels: Excellent, Good, Pass, and Fail. According to the test scores, an incomplete statistical graph was drawn as follows:
The frequency distribution table of physical education scores for the eighth grade (1) class:
\frac{} Based on the information provided by the statistical graph and table, answer the following questions:
(1) How many students are there in the eighth grade (1) class in total?
(2) Fill in the blanks: The frequency of Excellent physical education scores is ______, and the frequency of Pass scores is ______;
(3) Among the physical education scores of all students in the class, if a student's score is randomly selected, what is the probability that it is Pass or above (including Pass)? | 50 |
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<image>In a workshop of 120 workers, a random sample of 30 workers was taken to understand the number of parts processed daily by these workers. The survey results were organized, and an incomplete bar chart was drawn (as shown in the image). Based on the information in the graph, answer the following questions:
(1) Among the surveyed workers, the number of workers who process 9 parts per day is ______;
(2) Among the surveyed workers, the number of workers who process 12 parts per day is ______, the number of workers who process ______ parts per day is the highest, and the percentage of workers who process 15 parts per day among the surveyed workers is ______%;
(3) Based on the results of this survey, estimate the workshop's average number of parts processed per worker daily and the total number of parts processed daily in the workshop.
| 4 |
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<image>The results of a survey on the incidence of mulberry caterpillar dermatitis among mulberry pickers and auxiliary workers are shown in the table below: Use the independence test of the 2×2 contingency table to estimate whether "suffering from mulberry caterpillar dermatitis is related to mulberry picking." What is the probability of making a mistake if you believe there is a relationship between the two?
\frac{}
\frac{} | 0.1\% |
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<image>Last year, an unprecedented tsunami occurred in the Indian Ocean, bringing tremendous disaster to the countries around it. This calamity has touched the hearts of people all over the world, prompting many to generously donate to help those in the affected areas. The chart (1) below shows the donations made by students at a middle school in our city in the "Donating Love, Fighting Tsunami" campaign. Chart (2) shows the distribution of the student population at the school, which has a total of 1450 students.
(1) How much money did the ninth-grade students donate in total?
(2) What is the average donation per student at the school? (Please round to the nearest cent) | 2192.4 |
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<image>According to the "Road Traffic Safety Law of the People's Republic of China": If the blood alcohol concentration of a vehicle driver is between 20-80mg/100ml (excluding 80), it is considered driving after drinking; if the blood alcohol concentration is 80mg/100ml (including 80) or more, it is considered drunk driving. According to a report by "Legal Evening News," from March 15 to March 28, 2010, a total of 28,800 people nationwide were investigated for driving after drinking and drunk driving. The following frequency distribution histogram shows the blood alcohol concentration of these 28,800 people. The number of people falling under drunk driving is approximately ______. | 4320 |
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<image>The following is a statistical chart of telephone installations in a certain area.
(1) Estimate the number of landline telephones installed in this area in 1997 to be about _____.
(2) Predict the number of landline telephones to be installed in this area by 2005 to be about _____, and explain your reasoning. | 700 |
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<image>The average number of color TVs owned per hundred households in a certain region from 1997 to 2003 is shown in the figure:
(1) How many TVs does each small grid on the vertical axis represent?
(2) During which years was the growth rate the smallest?
(3) During which years was the growth rate the largest?
(4) What other mathematical questions can you pose? | 5 |
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<image>From a certain school, 20 classes are randomly selected to survey the number of people with online shopping experience in each class. The obtained data is shown in the stem-and-leaf plot and frequency distribution histogram.
(1) Find the value of $$m$$ in the frequency distribution histogram;
(2) If two classes are randomly selected from those with the number of people with online shopping experience in the interval [30, 40], find the probability that at least one of the classes has more than 36 people with online shopping experience. | 0.04 |
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<image>The education administrative department of a certain city conducted a random sampling survey to understand the participation of first-year junior high school students in comprehensive practical activities each semester. They collected data on the number of days students participated in these activities over a semester and used this data to create two incomplete statistical charts (as shown in the image).
Based on the information provided in the charts, please answer the following questions:
(1) Find the total number of first-year junior high school students in this school.
(2) In this survey, what are the mode and median respectively?
(3) If there are 6,000 first-year junior high school students in this city, estimate how many of them participated in “activities for no fewer than 4 days.” | 200 |
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<image>In response to the call for creating an environmentally friendly model city, a high school organized 1,200 students to participate in the voluntary collection of used batteries. The following chart represents the statistics of battery collection by 50 randomly selected students.
\frac{} Based on the data in the chart, answer the following questions:
(1) The average number of used batteries collected by each of these 50 students is ______ batteries;
(2) The median number of batteries is ______, and the mode is ______;
(3) Estimate the total number of batteries collected in this event by the school to be ______ batteries;
(4) According to the information, one button battery can pollute 600 tons of water, which is equivalent to a person's lifetime drinking water. Assuming that a button battery, a AAA battery, an AA battery, and a D battery pollute water in the ratio of 1:2:3:5, how many people's lifetime drinking water can be saved by this battery collection activity?
| 4.8 |
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<image>In order to understand the physical condition of the senior male students in a certain school, the weights (in kg) of all 480 senior male students were measured. The data falls within the interval [50,75], and the frequency distribution histogram is shown in the figure. If the frequency ratio of the first three groups from left to right in the figure is 1:2:3, then the number of senior male students whose weight is less than 60 kg is _______ _ | 180 |
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<image>To understand the weight situation of the students in our school who are preparing to apply for pilot this year, the data obtained has been organized into a frequency distribution histogram (as shown in the figure). It is known that the frequency ratio of the first three groups from left to right in the figure is 1:2:3, and the frequency of the second group is 12. The total number of students sampled is __________.
_ | 48 |
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<image>A city conducted a sample analysis of the math test scores for the middle school to high school entrance exam of that year. The maximum possible score for the test was 100 points. After organizing the scores (all integers), a statistical chart was created as shown in the figure. Based on the information provided in the figure, answer the following questions:
(1) How many students' math scores were sampled for analysis?
(2) If a score of 80 and above (including 80) is considered excellent, what is the estimated rate of excellent students for that year?
(3) The total number of students who took the middle school to high school math exam that year was 22,000. Estimate the number of students who scored at least 60 points.
| 300 |
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<image>A survey of monthly electricity consumption was conducted on 100 households from a certain community, and it was found that their electricity consumption ranged from 50 to 350 degrees. A frequency distribution histogram is shown below: (1) The value of x in the histogram is ___________; (2) The number of households with electricity consumption in the interval [100, 250) is ___________. __ | 0.0044 |
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<image>Below is a statistical chart showing the industrial wastewater discharge in our country from 2008 to 2011.
(1) How many billion tons more was the industrial wastewater discharge in our country in 2011 compared to 2008?
(2) What are your thoughts after looking at this statistical chart? | 80 |
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<image>Below is a statistical chart of the number of eggs laid by a hen over six months.
(1) Fill in the table based on the statistical chart.
\frac{}(2) What is the average number of eggs laid by this hen per month in the first half of the year?
(3) Can you come up with any other mathematical questions? Please provide solutions. | 24 |
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<image>In a class of 50 students, all the students have heights between 155cm and 185cm during a health check-up. The frequency distribution histogram of their heights is shown in the diagram. The number of students with heights between [170, 185] is ______.
| 22 |
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<image> The figure shows the frequency distribution polygon of the number of pulse beats per minute for 30 students. In the figure, the class midpoints of the two fictitious additional groups are ____ and ____, and the frequencies of these two groups are ____. | 65 |
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<image>To understand the physical development of students in a certain school, a sample of the weights of 100 high school boys was taken. Based on the obtained data, a frequency distribution histogram of the sample was drawn as shown in the figure. According to this figure, estimate the number of high school boys in the school weighing more than 70 kilograms out of a total of 2000 high school boys to be approximately ___.
| 600 |
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