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MM1G3c Proving Triangles Congruent (AAS, HL) 1 Postulates AAS If two angles and a non included side of one triangle are congruent to the corresponding two angles and side of a second triangle, then the two triangles are congruent. A B HL C E D A D F B C F E If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and corresponding leg of another right triangle, then the triangles are congruent. 2 Problem 1 Given: A C BE BD Prove: ABE CBD Step 1: Mark the Given Step 2: Mark vertical angles Step 3: Choose a Method (SSS /SAS/ASA/AAS/ HL ) Step 4: List the Parts in the order of the method Step 5: Fill in the reasons Statements Reasons Step 6: Is there more? Given AAS A C B E D 1. A C 2. ABE CBD Vertical Angle Thm 3. BE BD Given 4. ABE CBD AAS Postulate 3 Given: Problem 2 ABC, ADC right AB AD Prove: ABC ADC s Step 1: Mark the Given Step 2: Mark reflexive sides Step 3: Choose a Method (SSS /SAS/ASA/AAS/ HL ) Step 4: List the Parts in the order of the method Step 5: Fill in the reasons Statements Reasons Step 6: Is there more? 1. ABC , ADC Given HL A B C right s 2. AB AD D 3. AC AC Given Reflexive Property 4. ABC ADC HL Postulate 4