Segment AH is the height of triangle ABC in which angle C is 63 degrees and angle BAH is 27

Segment AH is the height of triangle ABC in which angle C is 63 degrees and angle BAH is 27 degrees. Prove that AB is equal to AC.

Given:

triangle ABC,

АН – height,

angle С = 63 degrees,

angle BAH = 27 degrees.

Prove that AB is equal to AC.

Evidence:

1. Consider a right-angled triangle AHC. Knowing that the sum of the degree measures of the triangle is 180 degrees, then the angle AHC + angle HCA + angle HAC = 180;

90 + HCA angle + 63 = 180;

153 + HCA angle = 180;

angle HCA = 180 – 153;

angle HCA = 27 degrees.

2. Consider a right-angled triangle ABH.

Angle ABH = 180 – 27 – 90;

angle ABH = 63 degrees.

3. Therefore triangle ABH = triangle AHC, then AB = AC. Q.E.D.