In triangle FGH, FG = 12.3 cm, GH = 10.6 cm, Measure of angle G = 80 degrees, and Measure of angle H = 55 degrees. If Triangle A

Response:

AB = 10.6 cm

Detailed breakdown:

In triangle FGH, FG measures 12.3 cm, GH is 10.6 cm, m angle G is 80 degrees, and m angle H is 55 degrees. If triangle ABC is congruent to triangle GHF, which of the following statements holds true?

A. AB = 12.3 cm

B. AB = 10.6 cm

C. m angle C = 55 degrees

D. m angle C = 80 degrees

Response:

Since triangle ABC ≅ GHF, it indicates that triangle ABC is congruent to triangle GHF.

For two triangles to be congruent, the length of their three sides and measures of their three angles must be identical.

Thus, the corresponding sides and angles in triangle FGH match those in triangle ABC.

AB = GH

AB = 10.6 cm

m∠F + m∠G + m∠H = 180° (total of angles in a triangle)

m∠F + 80 + 55 = 180

m∠F + 135 = 180

m∠F = 180 - 135 = 45

m∠F = 45°

m∠F is equal to m∠C

m∠C = 45°