Question

Geometry - Triangle d) In the given figure, BE = EC and CE is the bisector of ZACB. Prove that ZBEC = ZACD. E B D С​

Answer 1

Let m∠BCE = x

Then m∠ACE = x as well since CE is bisecting ∠ACB.

• m∠ACD + x + x = 180° ⇒
• m∠ACD = 180° - 2x

Consider ΔBEC

Since BE = EC, the opposite angles are congruent:

• ∠BCE ≅ ∠CBE

Then:

• m∠CBE = m∠BCE = x

Find the angle BEC:

• m∠BEC = 180° - (x + x) = 180° - 2x

Comparing the above we see that:

• m∠BEC = m∠ACD
• proved