Question

triangle congruence by sss and sas
guided practice
look at the figures. how can you prove these triangles are congruent?
a. \\( \triangle a b c \cong \triangle d e f \\) by the sas postulate.
b. it is not possible to determine if the triangles are congruent.
c. \\( \triangle a b c \cong \triangle d e f \\) by the sss postulate.

Explanation:

The SSS (Side - Side - Side) Postulate states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent. In the given figures, we can assume that the marked sides (the sides with the same number of tick - marks) are congruent. Since all three pairs of corresponding sides are congruent (as indicated by the tick - marks on each side of the two triangles), we use the SSS Postulate. The SAS (Side - Angle - Side) Postulate requires two sides and the included angle to be congruent. But there is no information about angles given here.

Answer:

C. \( \triangle ABC\cong\triangle DEF\) by the SSS Postulate.