You will learn to use the SSS and SAS tests for congruency.

1) Draw an acute scalene triangle on a piece of paper. Label its vertices A, B, and C, on the interior of each angle. A C B 2) Construct a segment congruent to AC. Label the endpoints of the segment D and E. DE F 3) Construct a segment congruent to AB. 4) Construct a segment congruent to CB. 6) Draw DF and EF. 5) Label the intersection F. This activity suggests the following postulate.

Postulate 5-1 SSS Postulate If three _____ of one triangle are congruent to _____ _____________ sides of another triangle, then the two Triangles are congruent. sides three corresponding A B C R S T If AC  RT and AB  RS andBC  ST then ΔABC  ΔRST

In two triangles, ZY  FE, XY  DE, and XZ  DF. Write a congruence statement for the two triangles. Z Y F E X D Sample Answer: ΔZXY  ΔFDE

In a triangle, the angle formed by two given sides is called the ____________ of the sides. included angle A B C  A is the included angle of AB and AC  B is the included angle of BA and BC  C is the included angle of CA and CB Using the SSS Postulate, you can show that two triangles are congruent if their corresponding sides are congruent. You can also show their congruence by using two sides and the ____________. included angle

Postulate 5-2 SAS Postulate If ________ and the ____________ of one triangle are congruent to the corresponding sides and included angle of another triangle, then the triangles are congruent. two sides included angle A B C R S T If AC  RT and  A   R and AB  RS then ΔABC  ΔRST

Determine whether the triangles are congruent by SAS.  If so, write a statement of congruence and tell why they are congruent.  If not, explain your reasoning. On a piece of paper, write your response to the following: P R Q F E D NO!  D is not the included angle for DF and EF.