Question

explain how you know that triangles are congruent. then write an equation and solve for x.

two triangles are shown. one triangle has a side labeled 8 in and an angle labeled 60 degrees. the other triangle has a side labeled (x - 3) in.

a. side - angle - side; x - 3 = 8.5
b. side - side - side; x - 3 = 8.11
c. side - angle - side; x - 3 = 8.11
d. side - side - side; x - 3 = 8.5

Explanation:

Step1: Identify congruence criterion

Since two - sides and the included angle of one triangle are equal to the corresponding two - sides and the included angle of the other triangle, the congruence criterion is Side - Angle - Side (SAS).

Step2: Set up equation

The corresponding sides are equal. If one side is 8.5 units and the other is \(x - 3\) units, then \(x-3 = 8.5\).

Answer:

A. Side - Angle - Side; \(x - 3=8.5\)