a We are given two triangles and want to justify the relationship between them. In both triangles we know two angles. We have also been given two sides in △ABC and one side in △EDF.
If two triangles have at least two pairs of , they are . Using the , we can find the measure of ∠A.
m∠A+39∘+25∘=180∘⇕m∠A=116∘
We can use the Triangle Angle Sum Theorem again to find the measure of
∠F.
39∘+116∘+m∠F=180∘⇕m∠F=25∘
As we can see,
△ABC and
△EDF have two pairs of congruent angles,
∠A and
∠E, and
∠C and
∠D. Therefore, the triangles are similar by the . To determine if the triangles are congruent, we must identify pairs of corresponding sides of the two triangles.
From the diagram we see that two pairs of corresponding angles — ∠A and ∠E, and ∠B and ∠F — and the side between them are congruent. Therefore, we can claim that the triangles are congruent by the . Let's show this as a .