Geometry Review CH4
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(2) Name: ________________________. ID: A. 5. ABC is an isosceles triangle. AB is the longest side with length 10x 4. BC = 5x 5 and CA = 4x 10. Find AB.. 6. One of the acute angles in a right triangle has a measure of 77.7 . What is the measure of the other acute angle? 7. Find m DCB, given. A. F, B . E, and m CDE 26.5 .. 8. Write an equation for the line perpendicular to the line shown that passes through the point (2, –3).. 9. How many sides must be congruent in an equilateral triangle?. 2.
(3) Name: ________________________. ID: A. 10. Write an equation for the line parallel to the line shown that passes through the point (5, -2).. 11. Write an equation for the line perpendicular to the line shown that passes through the point (5, -2).. Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 12. What proves. HJG . FJG? G. a. b. c. d.. F. J. H. ASA SAS SSS SSA. 3.
(4) Name: ________________________. ID: A. ____ 13. Which of the following is not a positioning of a right triangle with leg lengths of 5 units and 6 units? c. a.. b.. d.. ____ 14. Which pair of angle measures CANNOT be the acute angles of a right triangle? a. b. c. d.. 10 and 80 40 and 50 45 and 45 120 and 60. ____ 15. Given: A statement? a. b. c. d.. CBA BCA ABC BAC . F, B . D, C . E, AB DF , BC DE, and CA FE. Which is a correct congruence. DEF DEF DEF DEF. 4.
(5) Name: ________________________. ID: A. ____ 16. The transformation: x, y x 3, y 4 is a __________. a. Translation b. Rotation c. Reflection d. Dilation ____ 17. What type of triangle is. ABC ?. o. 50. o. a. b. c. d.. o. 63. 67. obtuse right acute equiangular. ____ 18. What additional information would allow you to prove the triangles congruent by SAS?. R K S. 44 L a. b. c. d.. M. T. M R M T M S K T. 5.
(6) Name: ________________________. ID: A. ____ 19. Which postulate or theorem can you use to prove. A. ABE . CDE?. B. E. D a. b.. C. AAS ASA. c. d.. ____ 20. What additional information will prove A B. ABE . SSS SAS. CDE by HL?. E. D a. b. c. d.. C. AE CE BE DE BE CE AB CD. ____ 21. Given: ABCD is a square with vertices A(0,0), B(0, 4), C(4, 4), and D(4,0). In a coordinate proof, what information would be used to prove AB CD if you do NOT use the distance formula? a. b. c. d.. y-coordinate of B, y-coordinate of C y-coordinate of A, x-coordinate of C x-coordinate of A, y-coordinate of C x-coordinate of A, x-coordinate of C. 6.
(7) Name: ________________________. ____ 22. If. a. b. c. d.. FGJ . ID: A. HGJ , what reason justifies the statement HG FG?. Reflex. Prop. of ASA CPCTC Def. of bisects. ____ 23. Classify DBC by its angle measures, given m DAB 60 , m ABD 75 , and m BDC 25 .. a. b.. obtuse triangle acute triangle. c. d.. right triangle equiangular triangle. c. d.. scalene triangle obtuse triangle. ____ 24. Classify ABC by its side lengths.. a. b.. equilateral triangle isosceles triangle. 7.
(8) Name: ________________________. ID: A. ____ 25. Find m K .. a. b.. m K = 63 m K = 55. c. d.. m K = 79 m K = 39. ____ 26. Given that ABC DEC and m E = 23°, find m ACB.. a. b.. m ACB = 77° m ACB = 67°. c. d.. 8. m ACB = 23° m ACB = 113°.
(9) Name: ________________________. ID: A. ____ 27. For these triangles, select the triangle congruence statement and the postulate or theorem that supports it.. a. b.. ABC JLK , HL ABC JKL, HL. c. d.. ABC JLK , SAS ABC JKL, SAS. ____ 28. Identify a pair of parallel segments.. a.. AB EH. c.. AB HG. b.. FB AB. d.. DH FG. c. d.. x1 x 2. ____ 29. Write and solve an inequality for x.. a. b.. x2 x2. 9.
(10) Name: ________________________. ID: A. ____ 30. Use the slope formula to determine the slope of the line.. a.. 0. b.. 3 2. c.. 2. d.. undefined. 10. 3.
(11) ID: A. Review Geometry Chapter 4 Test Answer Section SHORT ANSWER 1. 2. 3. 4. 5.. 115 25 12 25 AB = 54 Step 1 Find the value of x. BC CA. Step 2 Find AB. AB 10x 4. 5x 5. . 4x 10. . 10(5) 4. x. . 5. . 54. 6. 12.3 Let the acute angles be m M m N 90 77.7 m N 90 m N 12.3. M and N , with m M 77.7 . The acute angles of a right triangle are complementary. Substitute 77.7 for m M . Subtract 77.7 from both sides.. 7. m DCB 26.5 The Third Angles Theorem states that if two angles of one triangle are congruent to two angles of another triangle, then the third pair of angles are congruent. It is given that 1 3. 8. y = x –. A. F and B . E. Therefore, CDE . 11 3. 9. all 3 10. y = 3x - 17 11. y = 4x - 22 MULTIPLE CHOICE 12. B. 1. DCB. So, m DCB 26.5 ..
(12) ID: A 13. C These graphs show right triangles with leg lengths of 5 units and 6 units with one vertex at the origin.. This graph shows a right triangle with leg lengths of 5 units and 6 units with the base centered at the origin.. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23.. This graph shows an isosceles triangle that is not a right triangle.. D B A C B A B A C A. ABD and DBC form a linear pair, so they are supplementary. Therefore m ABD m DBC 180 . By substitution, 75 m DBC 180 . So m DBC 105 . DBC is an obtuse triangle by definition. 24. A From the figure AB AC . So, AB 8, and ABC is equilateral.. 2.
(13) ID: A 25. A m K m L m LMN. 6x 9 4x 7 118 10x 2 118 10x 120 x 12. m 26. B m m m m. Exterior Angle Theorem Substitute 6x 9 for m K , 4x 7 for m L, and 118 for m LMN . Simplify. Add 2 to both sides. Divide both sides by 10.. K 6x 9 6 12 9 63 DCE m CED m EDC 180 DCE 23 90 180 DCE 113 180 DCE 67. DCE . BCA. m DCE m BCA m ACB 67. Triangle Sum Theorem Substitution. Simplify. Subtract 113 from both sides. Corresponding parts of congruent triangles are congruent. Definition of congruent angles Corresponding parts of congruent triangles are congruent.. 27. B Because BAC and KJL are right angles, ABC and JKL are right triangles. You are given a pair of congruent legs AC JL and a pair of congruent hypotenuses CB LK . So a hypotenuse and a leg of ABC are congruent to the corresponding hypotenuse and leg of JKL. ABC JKL by HL. 28. C Parallel lines are coplanar and do not intersect. Segments are parallel if the lines that contain them are parallel. Also, parallel lines and segments are indicated by arrows on the drawing. 29. A DA DC DC is the shorter segment. 2x 4 8 Substitute 2x 4 for DA and 8 for DC . 2x 4 Subtract 4 from both sides. x2 Divide both sides by 2 and simplify. 30. B Substitute (6, –7) for (x 1 , y 1 ) and (9, –9) for (x 2 , y 2 ) in the slope formula. y 2 y 1 9 7 2 m x2 x1 96 3. 3.
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