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Warm-Up Exercises Lesson 4.5, For use with pages 249-255 Tell whether the pair of triangles is congruent or not and why. ANSWER Yes; HL Thm. Warm-Up1Exercises EXAMPLE Identify congruent triangles Warm-Up1Exercises EXAMPLE Identify congruent triangles Can the triangles be proven congruent with the information given in the diagram? If so, state the postulate or theorem you would use. SOLUTION a. The vertical angles are congruent, so two pairs of angles and a pair of non-included sides are congruent. The triangles are congruent by the AAS Congruence Theorem. Warm-Up1Exercises EXAMPLE Identify congruent triangles b. There is not enough information to prove the triangles are congruent, because no sides are known to be congruent. c. Two pairs of angles and their included sides are congruent. The triangles are congruent by the ASA Congruence Postulate. Warm-Up2Exercises EXAMPLE Prove the AAS Congruence Theorem Prove the Angle-Angle-Side Congruence Theorem. Write a proof. GIVEN PROVE A D, ABC C DEF F, BC EF Warm-Up Exercises GUIDED PRACTICE 1. for Examples 1 and 2 In the diagram at the right, what postulate or theorem can you use to RST VUT ? Explain. prove that SOLUTION STATEMENTS REASONS S U Given RS UV Given RTS UTV The vertical angles are congruent Warm-Up Exercises GUIDED PRACTICE for Examples 1 and 2 ANSWER UTV are congruent because Therefore RTS vertical angles are congruent so two pairs of angles and a pair of non included side are congruent. The triangle are congruent by AAS Congruence Theorem. Warm-Up Exercises GUIDED PRACTICE for Examples 1 and 2 Rewrite the proof of the Triangle Sum Theorem on page 219 as a flow proof. 2. ABC GIVEN PROVE m 1+m 2+m 3 = 180° STATEMENTS 1. Draw BD parallel to AC . 2. m 4 + m 2 + m 5 = 180° REASONS 1. Parallel Postulate 2. Angle Addition Postulate and definition of straight angle 3. 1 4, 3 4. m 1= m 4,m 5. m 1+m 2+m 3. Alternate Interior Angles 5 3= m 5 3 = 180° Theorem 4. Definition of congruent angles 5. Substitution Property of Equality Warm-Up3Exercises EXAMPLE Write a flow proof In the diagram, CE BD and CAB Write a flow proof to show GIVEN PROVE CE BD, CAB ABE ADE ABE CAD CAD. ADE Warm-Up4Exercises EXAMPLE Standardized Test Practice Warm-Up4Exercises EXAMPLE Standardized Test Practice The locations of tower A, tower B, and the fire form a triangle. The dispatcher knows the distance from tower A to tower B and the measures of A and B. So, the measures of two angles and an included side of the triangle are known. By the ASA Congruence Postulate, all triangles with these measures are congruent. So, the triangle formed is unique and the fire location is given by the third vertex. Two lookouts are needed to locate the fire. Warm-Up4Exercises EXAMPLE Standardized Test Practice ANSWER The correct answer is B. Warm-Up Exercises GUIDED PRACTICE 3. for Examples 3 and 4 In Example 3, suppose ABE ADE is also given. What theorem or postulate besides ASA can ABE ADE? you use to prove that ANSWER AAS Congruence Theorem. Warm-Up Exercises GUIDED PRACTICE 4. for Examples 3 and 4 What If? In Example 4, suppose a fire occurs directly between tower B and tower C. Could towers B and C be used to locate the fire? Explain ANSWER No triangle is formed by the location of the fire and towers, so the fire could be anywhere between towers B and C. Warm-Up Exercises Warm-Up Exercises Day one - 252: 1,2,4-7,9-13,18-20 Day two - 252: 14-17, 21,23-34