Assignment Assignment for Lesson.1 Name Date Constructing Congruent Triangles or Not Constructing Triangles In each exercise, do the following. a. Use the given information to construct a triangle. b. Determine whether it is possible to use the given information to construct another triangle that is not congruent to the first triangle. c. If it is possible to construct another triangle that is not congruent to the first triangle, construct it. If it is not possible, explain why not. 1. Use the two line segments and the included angle to construct X Y Z. X Y Y Z Y Chapter Assignments 105
2. Use the three angles to construct J K L. J K L 10 Chapter Assignments
Name Date 3. Use the two angles and the included side to construct M N P. N M M N Chapter Assignments 107
108 Chapter Assignments
Assignment Assignment for Lesson.2 Name Date Congruence Theorems SSS, SAS, ASA, and AAS 1. Complete the proof of the Angle-Side-Angle (ASA) Congruence Theorem. Given: A D, AC DF, C F Prove: ABC DEF B E C F A D Statements 1. A D, AC DF, C F 1. 2. ABC DEF 2. Reasons 3. A, E, C 3. Definition of Similar Triangles 4. AB DE BC EF AC DF 5. AC DF 5.. AC DF 7. AB 1 7. Substitution EF 8. AB DE, BC EF 8. 4.. Division Property of Equality 9. 9. Definition of Congruence 10. ABC DEF 10. Chapter Assignments 109
2. Write a two-column proof of the Angle-Angle-Side (AAS) Congruence Theorem. Given: A D, B E, BC EF, Prove: ABC DEF B E C F A D Write a Given statement and state the theorem that proves the triangles are congruent. Then write a congruence statement. 3. A C B E D 4. H M T A 110 Chapter Assignments
Name Date Determine the information that is needed to use the indicated theorem to show that the triangles are congruent. 5. FJG HJG by SAS. V W X Z Y X by AAS F J H Z W X Y G V 7. The figure shows a basic plan for a decorative porch roof. In the figure, DP is perpendicular to AG and AP PG. Use a two-column proof to show DPA DPG. D C E B F A P G Chapter Assignments 111
112 Chapter Assignments
Assignment Assignment for Lesson.3 Name Date Right Triangle Congruence Theorems HL, LL, HA, and LA Write a Given statement and state the theorem that proves the triangles are congruent. Then write a congruence statement. 1. G 2. M D H F X B T K Determine the information that is needed to use the indicated theorem to show that the triangles are congruent. 3. RQW RPW by HL Q R W 4. JNZ HNC by LA C N J H P Z Chapter Assignments 113
5. In the following figure, triangle ABD is an isosceles triangle and AC is perpendicular to BD. Use a two-column proof to show that B D. B C D A 114 Chapter Assignments
Assignment Assignment for Lesson.4 Name Date CPCTC Corresponding Parts of Congruent Triangles are Congruent 1. What is the width of the swimming pool? Explain how you got your answer. 82 ft 82 ft 84 ft 2. Marcel is painting the triangular section of a shuffleboard court shown in the figure. He starts by putting 41 feet of tape around the outside of the triangle. He knows that the base of the triangle is 1 feet and each base angle of the triangle measures 50 degrees. What is the length of each leg? 50 50 1 ft Chapter Assignments 115
Calculate the measure of angle 1. Show your work. 3. 4. 110 1 1 13 5. Use a two-column proof to show that LM bisects DF. L F Given: LF DM, DL MF Prove: LM bisects DF D X M 11 Chapter Assignments
Assignment Assignment for Lesson.5 Name Date Isosceles Triangle Theorems Isosceles Triangle Base Theorem, Vertex Angle Theorem, Perpendicular Bisector Theorem, Altitude to Congruent Sides Theorem, and Angle Bisector to Congruent Sides Theorem 1. Use the Isosceles Triangle Perpendicular Bisector Theorem to make a statement about isosceles CYX. X C D Y 2. Use the Triangle Base Theorem to make a statement about isosceles PBD. B P H D 3. Use the Isosceles Triangle Angle Bisector to Congruent Sides Theorem to make a statement about isosceles KSF. K S G T F Chapter Assignments 117
Solve for x. 4. (2x 7) K 5. S T RT = 7x 10 SV = 5x + 8 L (4x + 1) V B Q G R. 25 x 2 11 Z F D P 118 Chapter Assignments
Name Date 7. Use a flow chart proof to show that segment AY is B congruent to segment CZ. Given: AB CB, AXY CXZ Y Z Prove: AY CZ A C X Chapter Assignments 119
120 Chapter Assignments
Assignment Assignment for Lesson. Name Date Direct Proof vs. Indirect Proof Inverse, Contrapositive, Direct Proof, and Indirect Proof 1. Consider the conditional statement If a quadrilateral is a rectangle, then it is a parallelogram. a. Identify the hypothesis and the conclusion. b. Is the conditional statement true? Explain. c. Write the converse of the conditional statement. Is the converse true? Explain. d. Write the inverse of the conditional statement. Is the inverse true? Explain. e. Write the contrapositive of the conditional statement. Is the contrapositive true? Explain. Chapter Assignments 121
2. Consider the conditional statement If a triangle is equilateral, then the triangle is equiangular. a. Identify the hypothesis and the conclusion. b. Is the conditional statement true? Explain. c. Write the converse of the conditional statement. Is the converse true? Explain. d. Write the inverse of the conditional statement. Is the inverse true? Explain. e. Write the contrapositive of the conditional statement. Is the contrapositive true? Explain. 122 Chapter Assignments
Name Date 3. Use an indirect two-column proof to show that the complements of congruent angles are congruent. 3 1 4 2 Given: m 1 m 2, m 1 m 3 90, m 2 m 4 90 Prove: m 3 m 4 4. Write an indirect paragraph proof to show that an isosceles triangle cannot have a base angle that is a right angle. Chapter Assignments 123
124 Chapter Assignments