2. EXAMPLE 1 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 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. a.

3. EXAMPLE 1 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.

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

5. Example #2 – SAS – Postulate Given: N is the midpoint of LW N is the midpoint of SK Prove: N is the midpoint of LW N is the midpoint of SK Given Definition of Midpoint Vertical Angles are congruent SAS Postulate

6. Example #3 – ASA – Postulate Given: HA || KS Prove: HA || KS, Given Alt. Int. Angles are congruent Vertical Angles are congruent ASA Postulate

7. Example #4 – Paragraph Proof Given: Prove: is isosceles with vertex bisected by AH. Sides MA and AT are congruent by the definition of an isosceles triangle. Angle MAH is congruent to angle TAH by the definition of an angle bisector. Side AH is congruent to side AH by the reflexive property. Triangle MAH is congruent to triangle TAH by SAS. Side MH is congruent to side HT by CPCTC.

8. A line to one of two || lines is to the other line. Example #5 – Column Proof Given: Prove: Given has midpoint N Perpendicular lines intersect at 4 right angles. Substitution, Def of Congruent Angles Definition of Midpoint SAS CPCTC