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2 years ago

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

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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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