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Perpendicular Bisector

Based on the ...

Question

Based on the construction below, which of the given options must be true?

m ABD = m CBD

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m ABD = m CBD

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m ABD = m ABC

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m CBD = m ABD

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Solution

The correct option is A
m ABD = m CBD

The given construction clearly shows that BD bisects the $∠$ ABC.

Hence, m $∠$ ABC = 2m $∠$ ABD

m $∠$ ABD = m $∠$ DBC

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Similar questions

In the given figure $∠$ ADB = $∠$ CDB. If BD bisects $∠$ ABC, then which of the following is true ?

A B C D

A B = 6 c m, ∠ A = 60^{\circ}, ∠ A B D = 30^{\circ}

∠ C B D = 20^{\circ}

△ A B D

A B C D

A B = 6 c m, ∠ A = 60^{\circ}, ∠ A B D = 30^{\circ}

∠ C B D = 20^{\circ}

l (C D) = ?

seg A B ≅ seg C B and seg A D ≅ seg C D .

△ A B D ≅ △ C B D

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