加拿大数学10年级练习第一部分几何.doc

1. ABCD is an isosceles trapezoid, and . Which statement is NOT true? ABY BAX DXB DYB 2. It appears from the name of the HL Theorem that you actually need to know only two parts of a triangle in order to prove two triangles congruent. Is this the case? Yes, you only need to know the hypotenuse and a leg of a triangle. No, you actually need to know two sides and an angle, because the triangle must be a right triangle. No, you actually need to know three sides of the triangle. No, you actually need to know two angles and a side. 3. Complete the proof.Given: , 1 2, and .Prove: CEF AEF.BEC DEA by vertical angles. BEC DEA by (a)_. Then by CPCTC, . by the Reflexive Property. So CEF AEF by (b)_. a. SAS; b. SAS a. AAS; b. SSS a. ASA; b. SSS a. AAS; b. HL 4. Complete the proof.Given: , 1 2Prove: BEA DEC and 1 2, so BCA DAC by SAS. Then, since (a)_, , . BEA DEC by (b)_, so BEA DEC by (c)_. a. CPCTC; b. vertical angles; c. SAS a. CPCTC; b. vertical angles; c. AAS a. CPCTC; b. vertical angles; c. SSS a. SAS; b. vertical angles; c. SSS 5. What additional information can be used to prove the triangles congruent by the HL Theorem? mBCE = 90 AB AC 6. Suppose CED DBC. If mEDC = 63 and mDBC = 82, what is mDCE? 63 82 145 35 7. If A D and C F, which statement would NOT prove that ABC DEF? B E none of these 8. Determine what information you would need to know in order to use the SSS Congruence Postulate to show that the triangles are congruent. BAD CDB ADB CBD 9. Suppose BCA ECD. Which statement is NOT necessarily true? A D BCA DCE 10. In which triangles could you efficiently prove 1 2 using the HL Theorem? II only III only II and III I only 11. Complete the proof.Given: , 1 2, and .Prove: CEF AEF.BEC DEA with vetical angles. BEC DEA by (a)_. Then by (b)_, . by the Reflexive Property. So CEF AEF by (c)_. a. AAS; b. CPCTC; c. SSS a. SAS; b. CPCTC; c. SSS a. AAS; b. CPCTC; c. SAS a. SSS; b. CPCTC; c. ASA 12. In the paper airplane, ABCD EFGH, mB = mBCD = 90, and mBAD = 140. Find mGHE. 130 90 40 140 13. Find the value of x. x = 2 x = 9 x = 21 none of these 14. Explain how you can use SSS, SAS, ASA, or AAS with CPCTC to prove that D B. and ACB ACD. By the Symmetric Property, . By SAS, ABC ADC, so by CPCTC D B. and ACB ACD. By the Reflexive Property, . By ASA, ABC ADC, so by CPCTC D B. and ACB ACD. By the Reflexive Property, . By SAS, ABC ADC, so by CPCTC D B. and ACB ACD. By the Reflexive Property, . By SSS, ABC ADC, so by CPCTC D B. 15. Complete the proof.Given: bisects URS and bisects UTS.Prove: URT SRT. Reflexive property definition of angle bisector HL Theorem CPCTC 16. Complete the proof.Given: RSQ TSQ, RQS TQS.Prove: .RSQ TSQ is given, as is RQS TQS. By the Reflexive Property, .SRQ STQ by (a)_, so by (b)_. a. ASA; b. CPCTC a. HL; b. CPCTC a. SSS; b. CPCTC a. SAS; b. CPCTC 17. Determine which triangles are congruent by AAS using the information in the diagram below. ABF EDF ADC EBC ABE EDA ABE CBE 18. Complete the proof.Given: bisects EBC and bisects ECC.Prove:EBD CBD. Same-Side Interior Angles Theorem given SSS postulate Triangle Inequality Theorem 19. ABD CBD. Name the theorem or postulate that justifies the congruence. SAS AAS ASA none of these 1. Determine whether each quadrilateral can be a parallelogram. If not, write impossible.a. Two adjacent angles are right angles, but the quadrilateral is not a rectangle.b. All of the angles are congruent. a. impossible; b. parallelogram a. parallelogram; b. parallelogram a. parallelogram; b. impossible a. impossible; b. impossible 2. Which statement is true? All rectangles are squares. All quadrilaterals are squares. All quadrilaterals are parallelograms. All parallelograms are quadrilaterals. 3. Which statement can be used to determine whether quadrilateral XYZW must be a parallelogram? and and and XW = WZ and XY = YZ 4. Choose the best name for the parallelogram and find the measures of the numbered angles. Square; all numbered angles are equal to 45. Rhombus; all numbered angles are equal to 115. Rhombus; all numbered angles are equal to 25. Square; all numbered angles are equal to 50. 5. Given: quadrilateral ABCD with A(2, 3), B(2, 4), C(9, 0), D(5, 7). Then ABCD is a rectangle because the slopes of the sides in pairs are negative reciprocals. the product of the slopes of the diagonals is 1. the figure has four vertices. opposite sides have the same slope. 6. Given the parallelogram below, find coordinates for P, without using any new variables. (a c, b) (a + c, b) (c, b) (c, a) 7. Find the values of the variables for the rectangle. Then find the lengths of the sides. x = 7, y = 5; side lengths: 70, 45 x = 5, y = 7; side lengths: 33, 94 x = 5, y = 7; side lengths: 50, 63 x = 7, y = 5; side lengths: 45, 45 8. Determine whether the quadrilateral is a parallelogram. Explain. and Yes; if two opposite sides are congruent, then the quadrilateral is a parallelogram. No; if the diagonals of a quadrilateral bisect each other, this is not enough to prove that the quadrilateral is a parallelogram. No; if two opposite sides are congruent, this is not enough to prove that the quadrilateral is a parallelogram. Yes; if the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. 9. Can coordinate geometry be used to prove that opposite sides and in quadrilateral EFGH are congruent? Yes; use the Distance Formula to show that the diagonals are congruent. No; you can only show that EF is parallel to GH by using coordinate geometry. Yes; use the Distance Formula between vertices E and F, and between vertices G and H. No; you can only find the slopes of EF and GH by using coordinate geometry. 10. A square WXYZ has the vertices W(b, b), X(b, b), Y(b, b), and Z(b, b). Which vertex is in Quadrant II? W Z X Y 11. J and M are base angles of isosceles trapezoid JKLM. If mJ = 21x + 4, mK = 12x 8, and M = 14x + 10, find the value of x. 2 9 12. Suppose you are using coordinate geometry to prove that quadrilateral WXYZ is a square. Explain why no two sides should be parallel to the y-axis. The x-axis would intersect two sides of the square, so the coordinates of the corners would not be clear. Sides which are parallel to the y-axis would have an undefined slope, so you cannot prove numerically that these sides are parallel. Points on the sides which are parallel to the y-axis could have any y-value. The sides of the square which are parallel to the y-axis could be easily confused with the y-axis. 13. Find AM if PN = 8 and AO = 5. 8 3 13 5 14. Given square ABCD, where A = (0, a), B = (a, a), C = (0, 0), and D = (a, 0). To prove that the diagonal AD is times the length of side CD, first use _ to find that = a and = a. Therefore, the ratio = , or . the definition of isosceles triangle ACD the definition of right angle C the Distance Formula the definition of the origin C = (0, 0) 15. A farmer is building a fence for his yard. He is considering two designs, which are shown below. Explain why the quadrilaterals formed by the horizontal rails and the slanting boards are parallelograms in both designs. The horizontal rails are parallel to each other. A parallelogram has exactly one pair of parallel sides, so both quadrilaterals are parallelograms. The horizontal rails are congruent to each other. The slanting boards are all congruent to each other. A parallelogram has two pairs of adjacent sides, but opposite sides are not congruent, so both quadrilaterals are parallelograms. The horizontal rails are congruent to each other. The slanting boards are all congruent to each other. A parallelogram has four congruent sides, so both quadrilaterals are parallelograms. The horizontal rails are parallel to each other. The identical slanting boards all slant at the same angle, so the sides are parallel. A parallelogram has both pairs of sides parallel, so both quadrilaterals are parallelograms. 16. A rhombus is centered on the origin. One side of the rhombus goes through the points (a, 0) and (0, b). What are possible coordinates for one of the other sides? (a, 0), (a, 0) (b, 0), (0, a) (0, b), (0, b) (a, 0), (0, b) 17. If a quadrilateral is a parallelogram, then its opposite sides are _. perpendicular adjacent congruent none of these 18. Find the value of each variable in the parallelogram. m1 = 10x, m2 = x + y, and m3 = 18z. x = 9, y = 81, z = 5 x = 18, y = 167, z = 5 x = 18, y = 162, z = 10 x = 9, y = 86, z = 0 19. Complete _ for parallelogram EFGH. Then state a definition or theorem as the reason. ; because the angles of a parallelogram bisect each other ; because the diagonals of a parallelogram bisect each other ; because the diagonals of a parallelogram bisect each other ; because the angles of a parallelogram bisect each other 20. Which of the following sets of points represents a line segment in Quadrant III and its reflection in the x-axis? (Use the positive numbers a, b, c, d for the coordinates of the endpoints). (a, b), (c, d); reflection (a, b), (c, d) (a, b), (c, d); reflection (a, b), (c, d) (a, b), (c, d); reflection (a, b), (c, d) (a, b), (c, d); reflection (a, b), (c, d) 1. Solve for a and b. a = , b = a = , b = a = , b = a = , b = 2. State whether ADB CDB, and if so, identify the theorem that proves the triangles similar. yes, SSS yes, AA yes, SAS no 3. ABCDE GHJDF. Complete the congruence and proportion statements.a. H b. = a. B; b. AE a. E; b. DC a. E; b. AE a. B; b. DC 4. Write a similarity statement for the two triangles. VUT WXY TVU WXY TUV WXY TUV WYX 5. Find the geometric mean of 48 and 3. 9 25.5 12 16 6. The extendable ramp shown below is used to move crates of fruit to loading docks of different heights. When the horizontal distance AB is 4 feet, the height of the loading dock, BC, is 3 feet. What is the height of the loading dock, DE? 7 ft 9 ft 11 ft 6 ft 7. Find the geometric mean of 20 and 5. 10 4 12.5 25 8. In movies and television, the ratio of the width of the screen to the height is called the aspect ratio. Television screens usually have an aspect ratio of 4 : 3, while movie screens usually have an aspect ratio of 1.85 : 1. However, if a movie is made for television in Letterbox format, it retains the 1.85 : 1 aspect ratio and fills in the top and bottom parts of the screen with black bars. What would be the height of a movie in Letterbox format on a television screen that measures 25 inches along its diagonal? (Hint: First find the width and height of the television screen.) 13.51 in. 10.81 in. 15 in. 8.12 in. 9. Use the diagram to determine the height of the tree. 264 ft 72 ft 60 ft 80 ft 10. The two rectangles are similar.Which is a correct proportion between corresponding sides? = = = = 11. Use the Side-Splitter Theorem to find x given that | . 18 12 24 6 12. Find OM if bisects NLM, LM = 14, NO = 3, and LN = 4. Round your answer to the nearest hundredth, if necessary. 12.27 18.67 0.86 10.5 13. There is a law that the ratio of the width to length for the American flag should be 10 : 19. Which dimensions are NOT in the correct ratio? 20 by 38 in. 50 by 95 ft 20 by 44 ft 100 by 190 ft 14. If one measurement of a golden rectangle is 6.8 inches, which could be the other measurement? 8.418 in. 11.002 in. 1.618 in. 5.182 in. 15. If one measurement of a golden rectangle is 8.2 inches, which could be the other measurement? 9.818 in. 6.582 in. 1.618 in. 5.068 in. 16. Solve = . 20 19 15 24 17. Find OM if bisects NLM, LM =15, NO = 5, and LN = 11. Round your answer to the nearest hundredth, if necessary. 33 6.82 3.67 8.59 18. The width of a golden rectangle is 3 m, which is shorter than the length. What is the length? 1.85 m 2.32 m 3.64 m 4.85 m 19. Find and simplify the ratio of the length to the width of the rectangle.20. BGH SWQ. What are the pairs of corresponding sides? BG and SQ, BH and SW, GH and WQ BG and GB, SQ and QS, GH and HG BG and SW, BH and SQ, GH and WQ BG and WQ, BH and SW, GH and SQ 1. A building near Atlanta, Georgia, is 181 feet tall. On a particular day at noon it casts a 204-foot shadow. What is the suns angle of elevation at that time? 41.6 27.5 62.5 48.4 2. In right triangle ABC, sin A = . What is cos A? none of these 3. Find the ratio for cos x. 1 4. Find the value of x to the nearest meter. 46 m 40 m 35 m 36 m 5. Compare the quantity in Column A with the quantity in Column B. The diagram may not be drawn to scale. The quantity in Column A is greater. The quantity in Column B is greater. The two quantities are equal. The relationship cannot be determined on the basis of the information given. 6. How many of these triples could be sides of a right triangle: (27, 36, 45), (12, 17, 20), (24, 32, 40), (14, 48, 50)? 4 triples 3 triples 2 triples 1 triple 7. Find the ratio for cos x. 2 8. Find a third number of the Pythagorean triple that includes 72 and 75. 9 21 37 104 9. Find the measure of the marked acute angle to the nearest degree. 62 28 61 118 10. In ABC, A is a right angle and mB = 60. If AB = 20 ft, find BC. If necessary, round your answer to the nearest tenth. 10 ft. 40 ft 20 ft ft 11. Find the value of the variable to the nearest hundredth. 5.28 cm 0.32 cm 3.13 cm 5.12 cm 12. Find the length of the leg of the right triangle. Leave your answer in simplest radical form. 48 288 13. In ABC, A is a right angle and mB = 45. If AB = 20 ft, find BC. 10 ft 20 ft 40 ft 20 ft 14. Which direction bearing is shown? 19 north of east 19 north of west 19 south of east 19 south of west 15. Leslie used the diagram to compute the distance from Ferris to Dunlap to Butte. How much shorter is the distance directly from Ferris to Butte than the distance Leslie found? 123 mi 87 mi 36 mi 84 mi 16. Which vector has a direction of 31 east of north?17. Find the value of x to the nearest tenth. 14.4 6.3 7.8 3.1 18. Find the value of x. 3 6 12 6 19. Find the value of x to the nearest tenth. 7.8 18.3 33.0 8.9 20. Find the value of x to the nearest integer when tan x = 1.483. 58 56 55 57 1. Which type of isometry is the equivalent of two reflections across two vertical lines? translation rotation glide reflection none of these 2. A section of a tessellated plane is shown below. Which types of symmetry does the tessellated plane have? glide-reflectional symmetry translational, rotational, and glide-reflectional symmetry rotational symmetry translational and reflectional symmetry 3. A blueprint for a house has a scale of 1 : 30. A wall in the blueprint is 7 in. What is the length of the actual wall? 210 ft 21 ft 17.5 ft none of these 4. What is the image of the point (4, 2) after a rotation 270 clockwise about the origin? (4, 2) (4, 2) (2, 4) (2, 4) 5. Which graph shows a triangle and its reflection image in the x-axis?6. Write a rule to describe a reflection over the y-axis. (x, y) (x, y) (x, y) (x, y) (x, y) (x, y) (x, y) (y, x) 7. Which types of symmetry does the figure have? reflectional rotational rotational and reflectional none of these