Amber believes triangle abc and triangle gfe are congruent. she has recorded the measures of some of the angles and the lengths of some of the sides in the triangles below. what additional measurement would support amber’s hypothesis? a. the measure of c is 32 b. the measure of c is 40 c. the measure of c is 50 d. the measure of c is 90

If the triangles are congruent, the angle opposite the 32 cm side will have the same measure as angle E, 40°. An appropriate choice for this question is ...
  b. The measure of c is 40.


In actual fact, the triangles not only are not congruent, they cannot exist. The total of sides FG and FE (82 cm) is less than the length of side GE (38 in). 82 cm is about 32.3 inches, about 5.7 inches too short.

Even if you overlook the units problem, the sum of squares of the sides of the triangle is 32² +38² = 2468, somewhat short of 50² = 2500. That is, the largest angle is slightly more than 90°. It is closer to 90.754° ≈ 91°.

You can label a diagram any way you want, but that doesn't mean the numbers are consistent or sensible.