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IrinaVladis [17]
2 years ago
8

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

Mathematics
1 answer:
Llana [10]2 years ago
8 0

Answer:

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

<u>Since BE = EC, the opposite angles are congruent:</u>

  • ∠BCE ≅ ∠CBE

<u>Then:</u>

  • m∠CBE = m∠BCE = x

<u>Find the angle BEC:</u>

  • m∠BEC = 180° - (x + x) = 180° - 2x

<u>Comparing the above we see that:</u>

  • m∠BEC = m∠ACD
  • proved

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