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Proving Congruent Triangles Side-Side-Side Postulate (SSS) - If the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent. B A E C D F Side-Angle-Side Postulate (SAS) - If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent. B A E C D F Angle-Side-Angle Postulate (ASA) - If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent. B A E C D F Angle-Angle-Side Theorem (AAS) - If two angles and a nonincluded side of one triangle are congruent to the corresponding two angles and side of a second triangle, then the triangles are congruent. B A E C D F C.P.C.T.C. - Corresponding Parts of Congruent Triangles are Congruent Directions: Write a proof for each. 1. Given: (D ≅ (E D B C is the midpoint of DE C Prove: + DBC ≅+ EAC A Statement 1. (D ≅ (E E Reason 1. Given C is the midpoint of DE D 2. Given: DE bisects BA BA bisects DE C Prove: + DBC ≅+ EAC A Statement 1. DE bisects BA BA bisects DE B Reason 1. Given E 3. Given: + ABC is an isosceles triangle with vertex (ABC B D is the midpoint of AC Prove: + ABD ≅+CBD A Statement 1. + ABC is an isosceles triangle with vertex (ABC D C Reason 1. Given D is the midpoint of AC 4. Given: BD ⊥ AC B BD bisects AC Prove: + ABD ≅+CBD A Statement 1. BD ⊥ AC BD bisects AC Reason 1. Given D C 5. Given: AB & DC A B BC & AD Prove: (A ≅ (C D Statement 1. AB & DC C Reason 1. Given BC & AD 6. Given: (ADB ≅ (CBD A B DA ≅ BC Prove: AB ≅ CD D Statement 1. (ADB ≅ (CBD DA ≅ BC Reason 1. Given C 7. Given: (BDE ≅ (BED (A ≅ (C B AD ≅ CE Prove: + BAE ≅+ BCD A Statement 1. (BDE ≅ (BED (A ≅ (C D E C Reason 1. Given AD ≅ CE 8. Given: (ABE ≅ (CBD (A ≅ (C B AB ≅ CB Prove: + ABD ≅+CBE A Statement 1. (ABE ≅ (CBD (A ≅ (C AB ≅ CB Reason 1. Given D E C 9. Given: (ABD ≅ (CBE B (A ≅ (C AB ≅ CB Prove: AE ≅ CD A Statement 1. (ABD ≅ (CBE (A ≅ (C D E C Reason 1. Given AB ≅ CB B 10. Given: AE ≅ CD (A ≅ (C AB ≅ CB Prove: DB ≅ EB A Statement 1. AE ≅ CD (A ≅ (C AB ≅ CB Reason 1. Given D E C B 11. Given: + ABC is an isosceles triangle with base AC (BDE ≅ (BED (A ≅ (C Prove: + ABE ≅+CBD A Statement 1. + ABC is an isosceles triangle with base AC (BDE ≅ (BED D E C Reason 1. Given (A ≅ (C 12. Given: (ABE ≅ (DCE B C (EAD ≅ (EDA E Prove: BA ≅ CD A Statement 1. (ABE ≅ (DCE (EAD ≅ (EDA Reason 1. Given D 13. Given: (A ≅ (ABE B C (ECD ≅ (D (A ≅ (D AE ≅ DE A D Prove: + BEC is an isosceles triangle E Statement 1. (A ≅ (ABE (ECD ≅ (D (A ≅ (D AE ≅ DE Reason 1. Given