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Example 1

Example 1. You are given that  R   Y and  S   X. b. You know that RT  YZ , but these sides are not included between the congruent angles, so you cannot use the ASA Congruence Postulate. Determine When To Use ASA Congruence.

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Example 1

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  1. Example 1 You are given that R Y and S X. b. You know that RTYZ,but these sides are not included between the congruent angles, so you cannot use the ASA Congruence Postulate. Determine When To Use ASA Congruence Based on the diagram, can you use the ASA Congruence Postulate to show that the triangles are congruent? Explain your reasoning. a. b. SOLUTION You are given that C E,B F, andBC FE. a. You can use the ASA Congruence Postulate to show that ∆ABC ∆DFE.

  2. Example 2 Determine What Information is Missing What additional congruence is needed to show that∆JKL∆NMLby the AAS Congruence Theorem? SOLUTION You are given KLML. BecauseKLJ andMLN are vertical angles,KLJ MLN.The angles that makeKL and ML the non-includedsidesareJ andN, so you need to know that J  N.

  3. Example 3 SOLUTION EFJH Given a. Decide Whether Triangles are Congruent Does the diagram give enough information to show that the triangles are congruent? If so, state the postulate or theorem you would use. a. b. c. E  J Given FGE  HGJ Vertical Angles Theorem Use the AAS Congruence Theorem to conclude that ∆EFG  ∆JHG.

  4. Example 3 Based on the diagram, you know only that MPQN and NPNP.You cannot conclude that the triangles are congruent. b. WZWZ Decide Whether Triangles are Congruent b. c. UZW  XWZ c. Alternate Interior Angles Theorem Reflexive Prop. of Congruence UWZ  XZW Alternate Interior Angles Theorem Use the ASA Congruence Postulate to conclude that ∆WUZ  ∆ZXW.

  5. A step in the Cat’s Cradle string game creates the triangles shown. Prove that ∆ABD  ∆EBC. 2. Given A C B BD  BC, AD || EC E D ∆ABD ∆EBC Statements Reasons 1. Given 1. BD  BC 2. AD || EC Example 4 Prove Triangles are Congruent SOLUTION 3. Alternate Interior Angles Theorem 3. D  C 4. Vertical Angles Theorem ABD  EBC 4. 5. ∆ABD  ∆EBC 5. ASA Congruence Postulate

  6. Checkpoint 1. Complete the statement: You can use the ASA Congruence Postulate when the congruent sides are between the corresponding congruent angles. Decide Whether Triangles are Congruent _____ ? Does the diagram give enough information to show that the triangles are congruent? If so, state the postulate or theorem you would use. ANSWER included 3. 4. 2. yes; AAS Congruence Theorem ANSWER ANSWER ANSWER no no

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