In quadrilateral $A C B D$ , $A C = A D$ and $A B$ bisects $∠ A$ (see figure). Show that $△ A B C ≅ △ A B D$ . What can you say about $B C$ and $B D$ ?

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Solution

In $Δ A C B$ and $Δ A D B$ ,
Side $A B =$ Side $A B$ [common side]
$∠ C A B = ∠ D A B$ [definition of angle bisector]
side $C A =$ side $D A$ [Given]

Therefore, By SAS test, we say that $Δ A C B ≅ Δ A D B$

Thus, the corresponding sides of congruent triangles are equal.

Hence, $B C = B D$

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Similar questions

In quadrilateral $A C B D$ , $A C = A D$ and $A B$ bisects $∠ A$ (see Fig). Show that $△ A B C ≅ △ A B D$ . What can you say about $B C$ and $B D$ ?

∠ A

△ A B C ≅ △ A B D

∠

Δ A B C ≅ Δ A B D .

In quadrilateral $A C B D, A C = A D$ and $A B$ bisects $∠ A$ . Show that $△ A B C ≅ △ A B D$ . What can you say about $B C$ and $B D$ ?

∠

Δ A B C ≅ Δ A B D .

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