Question

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

Explanation:

Step1: Identify corresponding sides

From the figure, \(AB = AC\) (marked with two - line segments), \(BD=CD\) (marked with one - line segment), and \(AD = AD\) (common side).

Step2: Apply SSS Postulate

The SSS (Side - Side - Side) Postulate states that if three sides of one triangle are equal to three sides of another triangle, then the two triangles are congruent. Here, in \(\triangle ABD\) and \(\triangle ACD\), we have \(AB = AC\), \(BD = CD\), and \(AD=AD\).

Answer:

B. \(\triangle ABD\cong\triangle ACD\) by the SSS Postulate.