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ANSWER

Tell whether the pair of triangles is congruent or not and why. Yes; HL Thm. ANSWER. Lesson 4.5 , For use with pages 249-255. EXAMPLE 1. Identify congruent triangles.

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ANSWER

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  1. Tell whether the pair of triangles is congruent or not and why. Yes; HL Thm. ANSWER Lesson 4.5, For use with pages 249-255

  2. EXAMPLE 1 Identify congruent triangles

  3. Can the triangles be proven congruent with the information given in the diagram? If so, state the postulate or theorem you would use. 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. EXAMPLE 1 Identify congruent triangles SOLUTION

  4. There is not enough information to prove the triangles are congruent, because no sides are known to be congruent. Two pairs of angles and their included sides are congruent. The triangles are congruent by the ASA Congruence Postulate. EXAMPLE 1 Identify congruent triangles

  5. C F, BC EF A D, GIVEN ABCDEF PROVE EXAMPLE 2 Prove the AAS Congruence Theorem Prove the Angle-Angle-Side Congruence Theorem. Write a proof.

  6. In the diagram at the right, what postulate or theorem can you use to prove that ? Explain. RSTVUT STATEMENTS REASONS Given S U Given RS UV The vertical angles are congruent RTSUTV for Examples 1 and 2 GUIDED PRACTICE SOLUTION

  7. RTSUTV for Examples 1 and 2 GUIDED PRACTICE ANSWER Therefore are congruent because 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.

  8. ABC GIVEN m 1 + m 2 + m 3 = 180° PROVE STATEMENTS REASONS Rewrite the proof of the Triangle Sum Theorem on page219as a flow proof. 1. Parallel Postulate 1. Draw BDparallel to AC. 2. m 4 + m 2 + m 5 2. = 180° Angle Addition Postulate and definition of straight angle , 4 3. 1 5 3. 3 Alternate Interior Angles Theorem m 4 m 5 4. m 1 = , m 3 = 4. Definition of congruent angles 5. m 1 + m 2 + m 3 5. Substitution Property of Equality = 180° for Examples 1 and 2 GUIDED PRACTICE

  9. GIVEN CE BD, ∠ CAB CAD ABEADE PROVE EXAMPLE 3 Write a flow proof In the diagram,CE BDand∠ CAB CAD. ABEADE Write a flow proof to show

  10. EXAMPLE 4 Standardized Test Practice

  11. The locations of tower A, tower B, and the fire form a triangle. The dispatcher knows the distance from tower A to tower Band the measures of Aand B. So, the measures of two angles and an included side of the triangle are known. EXAMPLE 4 Standardized Test Practice 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.

  12. EXAMPLE 4 Standardized Test Practice ANSWER The correct answer is B.

  13. ANSWER AAS Congruence Theorem. for Examples 3 and 4 GUIDED PRACTICE In Example 3, suppose ABEADEis also given. What theorem or postulate besides ASA can you use to prove that ABEADE?

  14. 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. for Examples 3 and 4 GUIDED PRACTICE

  15. Day one - 252: 1,2,4-7,9-13,18-20 Day two - 252: 14-17, 21,23-34

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