CONGRUENT TRIANGLES

1. CONGRUENT TRIANGLES Sections 4-4

2. SSS If three sides of one triangle are congruent to three sides of another triangle, the triangles are congruent. Methods of Proving Triangles Congruent SAS If two sides and the included angle of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent. ASA If two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent. AAS If two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent. HL If the hypotenuse and leg of one right triangle are congruent to the corresponding parts of another right triangle, the right triangles are congruent.

3. Congruent Triangles Name the congruence Is ? FRS PQD R P 120° Q F 120° 35° D 35° ASA S

4. Congruent Triangles Name the congruence Is QSR ? FRS R Q 42° 42° F Shared Side – Reflexive Prop S WHY NOT? SSA SSA is NOT a valid Triangle congruence

5. Congruent Triangles Name the congruence Is ? FRS QSR R 50° Q F Shared Side – Reflexive Prop 50° S SAS

6. Congruent Triangles Name the congruence Is ? MNR PTB B R N P SSS ? T M WHY NOT? Names of the triangles in the congruence statement are not in corresponding order.

7. A C Writing a PROOF B Given: AB = BD EB = BC Prove: ∆ABE ˜ ∆DBC 1 2 = SAS E D

8. A C Given: AB = BD EB = BC Prove: ∆ABE ≅ ∆DBC B 1 2 SAS E D STATEMENTS REASONS AB ≅ BD Given <1 ≅ <2 VA EB ≅ BC Given ∆ABE ≅ ∆DBC SAS

9. C Given: CX bisects ACB A ≅ B Prove: ∆ACX≅∆BCX 2 1 AAS B A X CX bisects ACB Given 1 ≅ 2 Def of angle bisector A ≅ B Given CX ≅ CX Reflexive Prop ∆ACX ∆BCX AAS ≅

10. Can you prove these triangles are congruent? A Given: AB llDC; X is the midpoint of AC Prove: AXB ˜ CXD B X = D C

11. A B X Given: AB ll DC X is the midpoint of AC Prove: AXB ˜ CXD D C = ASA