Triangle Congruence Problem: Proving Congruence with 120° Angles and Sides of 16 and 9

Question

Are the triangles shown in the diagram congruent? If so, according to which congruence theorem?

120°120°120°120°120°120°161616999161616999AAABBBCCCGGGFFFDDD

Step-by-Step Solution

To answer the question, we need to know the fourth congruence theorem: S.A.S.

The theorem states that triangles are congruent when they have an equal pair of sides and an equal angle.

However, there is one condition: the angle must be opposite the longer side of the triangle.

 

We start with the sides:

DF = CB = 16
GD = AC = 9

Now, we look at the angles:

A = G = 120

We know that an angle of 120 is an obtuse angle and this type of angle is always opposite the larger side of the triangle.

Therefore, we can argue that the triangles are congruent according to the S.A.S. theorem.

 

Answer

Congruent according to S.A.S.