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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 You are given that R Y and S X. b. You know that RTYZ,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.
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 KLML. BecauseKLJ andMLN are vertical angles,KLJ MLN.The angles that makeKL and ML the non-includedsidesareJ andN, so you need to know that J N.
Example 3 SOLUTION EFJH 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.
Example 3 Based on the diagram, you know only that MPQN and NPNP.You cannot conclude that the triangles are congruent. b. WZWZ 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.
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
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