vishakhasingha
Answered

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

Geometry Triangle D In The Given Figure BE EC And CE Is The Bisector Of ZACB Prove That ZBEC ZACD E B D С class=

Sagot :

mhanifa

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

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

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