Question

Drawing Conclusions about Triangles
Consider the triangles.

Triangle G H I. Side G H is 16 inches, H I is 15 inches, G I is 10 inches. Angle G is 65 degrees, H is 48 degrees, I is 67 degrees. Triangle D E F. Side D E is 3 inches, E F is 3.2 inches, D F is 2 inches. Angle D is 67 degrees, E is 48 degrees, F is 65 degrees.

What can be concluded about these triangles? Check all that apply.
The corresponding angles are proportional.
The ratios of the corresponding sides are equivalent.
The corresponding sides are congruent.
The corresponding angles have the same measure.
DE corresponds to IH.

Answer 1

Correct conclusions:
- The ratios of the corresponding sides are equivalent. (True — each side of GHI is 5 times the matching side of DEF: 16/3.2 = 15/3 = 10/2 = 5.)
- The corresponding angles have the same measure. (True — G=65° matches F=65°, H=48° matches E=48°, I=67° matches D=67°.)
- DE corresponds to IH. (True — D↔I and E↔H, so segment DE corresponds to IH.)

Not correct:
- The corresponding sides are congruent. (False — corresponding side lengths are proportional by factor 5, not equal.)
- The corresponding angles are proportional. (This phrasing is misleading; angles are equal, so their measures have ratio 1, but the usual correct statement is that corresponding angles are congruent / have the same measure. So treat this as not the intended correct choice.)