Choose the best answer. 1. Which of PQ and QR contains P? A PQ only B QR only C Both D Neither. K is between J and L. JK 3x, and KL x 1. If JL 16, what is JK? F 7 H 9 G 8 J 13 3. SU bisects RST. If mrst (8x 1) and mrsu x, what is mrst? A C 0 B 37. D 7 4. If the complement of an angle measures, what is the measure of its supplement? F 68 H 11 G 78 J 18. The perimeter of a square is 8 meters. What is its area? A 4 m C 16 m B 8 m D 64 m 6. What is the area of a circle whose diameter is 3 centimeters? F 1. cm H 6 cm G. cm J 36 cm 7. The midpoint of a segment is (, ), and one of the endpoints is (3, 6). Where is the other endpoint? A (1, 16) C (., 0.) B (4, 17) D (0.,.) 8. Where is the image of (6, ) reflected across the graph of y x? F (, 6) H (, 6) G (, 6) J (, 6) 9. What is the next term in the sequence? 79, 43, 81, 7,... A 9 C 3 B 3 D 9 10. For which conditional statement (p q) is its converse (q p) false? F If a fruit has seeds inside, then it is an orange. G If Meg lives in Egypt, then she lives in Africa. H If the day is between Monday and Wednesday, then it is Tuesday. J If the car will not start, then it is out of gas. 11. For which conditional statement (p q) is its inverse (p q) false? A If a point is a midpoint of a segment, then it divides the segment into two congruent segments. B If Mike does not become an airplane pilot, then he will not learn how to fly a plane. C If you see a zebra, then you must be in a zoo. D If the biggest holiday of the month is Thanksgiving, then the month is November. 1. Which justifies the statement? If 1 and 3, then 1 3. F Transitive Property of Congruence G Substitution H Symmetric Property of Congruence J Reflexive Property of Congruence 101 Holt Geometry
13. Which is the most logical conclusion by the Law of Syllogism? If one of the angles of a triangle is obtuse, then the other two angles are acute. If a triangle is an obtuse triangle, then one of its angles is obtuse. A triangle has two acute angles. A The triangle is obtuse. B The other angle in the triangle is obtuse. C The triangle is not obtuse. D None of these are valid conclusions. 14. Which is a true biconditional statement? F Four points are coplanar if and only if they are noncollinear. G Two angles are complementary if and only if the sum of their measures is 90. H A side of a triangle is a hypotenuse if and only if it is the longest side of a triangle. J A figure has an endpoint if and only if the figure is a segment. 1. Complete the proof. Given: x Prove: (x ) 0 Statements Reasons 1. x 1. Given. x 0. Add. Prop. of 3. (x + ) 0 3.? A Multiplication Property of Equality B Transitive Property of Equality C Subtraction Property of Equality D Reflexive Property of Equality 16. Complete the statement. Two lines are parallel if the same-side interior angles are angles. F complementary H congruent G supplementary J corresponding 17. Which angles are alternate interior angles? 1 8 3 7 4 6 A 1 and 4 B 1 and 18. Complete the proof. Given: k Prove: 1 and 6 are supplementary. C 3 and 4 D 3 and 7 1 8 3 7 4 6 Statements Reasons 1. k 1. Given. 1.? 3. m1 m 3. Def. of 4. and 6 are 4. Linear Pair Thm. supplementary.. m m6. Def. of supp. 180 6. m1 m6 180 7. 1 and 6 are supplementary. 6. Subst. 7. Def. of supp. F Alternate Exterior Angle Theorem G Alternate Interior Angle Theorem H Same-Side Interior Angle Theorem J Corresponding Angle Theorem 10 Holt Geometry
19. A line passes through the points (, 8) and (6, ). What is the slope? A 10 C 1 10 B 6 D 10 11 0. Complete the paragraph proof. Given: Prove: 1 4 3 4 1 8 7 6 It is given that. By the Linear Pair Theorem, m m1 180 and. By the Congruent Supplements Theorem, 1 4. F m m3 180 G m4 m7 180 H m4 m 180 J m6 m7 180 1. Find all values for x. 10 4 A x 11 C 4 x 11 B 0 x 11 D x 3. What is the slope of the line perpendicular to y 3 x 9? F 3 H 3 G 3 7 J 3 3. What is the equation of the line that passes through (0, ) and (4, 6)? A y x C y x 4. Three sides of a triangle are shown. Which triangle is acute? F 3, 4, H 4,, 6 G, 1, 13 J 4, 7, 10. Find y. ( 6) A 36 B 8 ( 10) C 18 D 134 6. Which line coincides with the graph of 6x 10y 30? F y 3 x 3 H y 3 x G y 3 x 3 J y 3 x 7. Complete the statement. If U P, S Q, T R, UT PR, US PQ, and ST QR, then PQR. A RQP C TUS B STU D UST 8. What is the least information needed to prove the triangles congruent by SSS? F M Q G LN PR H LN PR and MN QR J LN QR and MN PR B y 1 x D y x 103 Holt Geometry
9. Why is PQS RQS? A SAS B ASA C AAA D HL 30. Complete the proof. Given: ABC is equilateral, and BD is an altitude. Prove: BD bisects AC. CB, By definition of equilateral, AB and by the Reflexive Property of Congruence, BD BD. Since BD is an altitude, BDA and BDC are right angles. So BDA and BDC are right and BDA BDC by HL. Therefore, AD CD by?. By definition of bisector, BD bisects AC. F HL H ASA G SAS J CPCTC 31. Given: TUVW is a rectangle. Prove: TV UW For an analytic proof, which is the best placement of the rectangle in the coordinate plane? A T(0, 0), U(a, b), V(0, c), W(a, c b) B T(0, 0), U(a, 0), V(a, b), W(0, b) C T(a, b), U(a b, 0), V(a b, c), W(0, c) D T(0, 0), U(a, 0), V(a, a), W(0, a) 3. One of the base angles of an isosceles triangle is 40. Which is the triangle classification according to its angles? F acute H obtuse G right J equiangular 33. QS bisects PQR. What is QR? 10 3 16 A 6 C 40 B 0 D 1 34. XL, XM, and XN are perpendicular bisectors. The perimeter of FGH is 4. What is FG? F 36 H 18 G 7 J 9 3. SV and RT are medians. What is JS JT? A x y C y 1 x B x 3y D 1 x y 36. In JKL, JK JL KL. Which is the correct order of the angles from smallest measure to largest? F J, L, K H K, L, J G J, K, L J L, K, J 37. Two sides of a 30-60-90 triangle are 9 and 18. What is the length of the third side? A 9 C 18 B 9 3 D 18 3 38. PQ is a midsegment. What is PQ? 17 16 17 16 F 16 H 3 G 17 J 34 104 Holt Geometry
Answer Key 17. 4 cm 18. 88 3 in or about 498.8 in Performance Assessment 1. Perpendicular Bisector Theorem. B is the midpoint of AC since BE is a midsegment. 3. 90; Def. of perpendicular bisector 4. BDC, DBE, EDB, ABE, A. AE AB; AEB 90, ABE 4, and, if two angles in a triangle are not congruent, then the longer side is opposite the larger angle. 6. The triangles are not congruent. The reasoning in the answer for question can be used to show that AB AE and AB EB and likewise that DC BC. But since AB BC, it follows that DC is longer than each side of ABE. Therefore ABE cannot be congruent to CDB. 7. a. 14 b. 14, or about 19.8 c. 8 d. 8, or about 39.6 1. C 0. H. F 1. C 3. D. G 4. H 3. A. A 4. H 6. G. B 7. A 6. F 8. J 7. D 9. D 8. H 10. G 9. B 11. C 30. J 1. F 31. B 13. D 3. H 14. G 33. A 1. A 34. H 16. G 3. C 17. D 36. G 18. F 37. B 19. D 38. G 6 Section Quiz: Lessons 6-1 Through 6-3 1. D 6. F. H 7. B 3. D 8. J 4. H 9. B. A Section Quiz: Lessons 6-4 Through 6-6 1. A 6. G. J 7. D 3. A 8. J 4. J 9. A. A Chapter Test Form A: Multiple Choice 1. D 9. C. C 10. A 3. A 11. A 4. D 1. B. A 13. B 6. A 14. A 7. B 1. A 8. A 16. A 61 Holt Geometry