Question

Given ac is perpendicular to cb and cx is perpendicular to ab, prove angle 2 is congruent to angle 3.

Answer 1

Explanation:

Given in the question,

AC ⊥ BC and CX ⊥ AB

m∠ACB = 90°

m∠ACX = 90° - m∠3

Now by applying the property of interior angle of triangle,

m∠CAX + m∠CXA + m∠ACX = 180°

m∠2 + 90° + (90°- m∠3) = 180°

m∠2 + 180° - m∠3 = 180°

m∠2 - m∠3 = 0

m∠2 = m∠3

Therefore, m∠2 ≅ m∠3.