Question

Generating Conclusions
Triangle E F G. Side E F is 6 meters, F G is 5 meters, E G is 7 meters. Angle F is 87 degrees and angle G is 58 degrees. Triangle K L J. Side K L is 28 meters, L J is 24 meters, J K is 20 meters. Angle K is 58 degrees, L is 35 degrees, J is 87 degrees.

What can you conclude about these triangles? Check all that apply.
Angle E corresponds to angle L.
All corresponding angles are proportional.
The measure of angle E is 29°.
The two triangles are similar.
The two triangles are congruent.

Answer 1

True:
- Angle E corresponds to angle L. (E = 35°, L = 35°.)
- The two triangles are similar. (All corresponding angles are equal and corresponding sides are in the same ratio: 24/6 = 20/5 = 28/7 = 4.)

False:
- All corresponding angles are proportional. (Corresponding angles are congruent/equal, not usually described as “proportional”; the intended correct statement is that corresponding sides are proportional.)
- The measure of angle E is 29°. (Angle E = 180 − 87 − 58 = 35°.)
- The two triangles are congruent. (Sides are in ratio 4, so the triangles are similar but not congruent.)