Question

In triangle GHJ , m angle H=110 , m angle J=40 , and I is the point on overline GJ that makes overline HI bisect GHJ. What is the longest side of triangle HIJ ?

Answer 1

In triangle GHJ, if m angle H = 110 and m angle J = 40, then m angle G = 180 - (110 + 40) = 30. Since angle I is the angle bisector of angle GHJ, the ratio of the length of side HI to the length of side HJ is equal to the ratio of the length of side GI to the length of side GJ.

Since the longest side of a triangle is opposite to the largest angle, the longest side of triangle HIJ is GJ.