Question

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

Explanation:

Step1: Analyze the given figure

From the figure, we can observe that \(AB = DC\) (marked as equal), \(AC = DB\) (marked as equal), and \(BC\) is a common side for \(\triangle ABC\) and \(\triangle DCB\).

Step2: Apply the 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.
In \(\triangle ABC\) and \(\triangle DCB\), we have \(AB = DC\), \(AC = DB\), and \(BC=CB\) (common side).

Answer:

B. \(\triangle ABC\cong\triangle DCB\) by the SSS Postulate.