Chapter 4: Congruent Triangles Lesson 4 and 5: Proving Congruence- SSS, SAS, ASA, AAS, and HL

SSS Side-Side-Side If all three sets of corresponding sides are congruent, the triangles are congruent A M B C N O ABC MNO

SAS Side-Angle-Side If two corresponding sides and the included angles of two triangles are congruent, then the triangles are congruent * The included angle is the angle between the congruent sides X F Y Z G H XYZ FGH

ASA Angle-Side-Angle If two sets of corresponding angles and the included sides are congruent, then the triangles are congruent * The included side is the side between the two congruent angles J R L K T S JKL RST

AAS Angle-Angle-Side If two sets of corresponding angles and one of the corresponding non-included sides are congruent, then the triangles are congruent T E G F V U EFG TUV

HL Hypotenuse-Leg If the hypotenuse and one set of corresponding legs of two right triangles are congruent, then the triangles are congruent C R D H A M CDH RAM

Determine if the triangles are congruent Determine if the triangles are congruent. If they are, write the congruence statement.

Determine if the triangles are congruent Determine if the triangles are congruent. If they are, write the congruence statement.

Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove congruence, choose not possible.

Given: AC  AB D is the midpoint of BC. Prove: ΔADC  ΔADB ___

Determine whether ΔABC  ΔDEF for A(–5, 5), B(0, 3), C(–4, 1), D(6, –3), E(1, –1), and F(5, 1).

Day #2- with a partner Write a two column proof.