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Byju's Answer

Standard VII

Mathematics

Side Side Side or S-S-S Congruence

For an isosce...

Question

For an isosceles triangle $A B C$ , such that $A B = A C$ and $A D$ is the bisector of $B C$ , then $Δ A D B ≅ Δ A D C$ ?

Yes

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Solution

The correct option is A Yes
For the given isosceles triangle $A B C$ .
$A D$ is the bisector of $B C$ .
$\Rightarrow B D = C D$
Also, $A B = A C$ and $A D$ is the common side.
$∴$ By S - S - S congruency
$Δ A D B ≅ Δ A D C$ .

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Similar questions

Q. In

Δ

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In ΔABC, AD is the perpendicular bisector of BC (see the given figure). Show that ΔABC is an isosceles triangle in which AB = AC.

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Question 2
In $Δ A B C, A D$ is the perpendicular bisector of BC (see the given figure).
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For an isosceles triangle ABC, such that AB=AC and AD is the bisector of BC, then ΔADB≅ΔADC?

The correct option is A YesFor the given isosceles triangle ABC. AD is the bisector of BC. ⇒BD=CD Also, AB=AC and AD is the common side. ∴ By S - S - S congruency ΔADB≅ΔADC.

For an isosceles triangle $A B C$ , such that $A B = A C$ and $A D$ is the bisector of $B C$ , then $Δ A D B ≅ Δ A D C$ ?

The correct option is A Yes
For the given isosceles triangle $A B C$ .
$A D$ is the bisector of $B C$ .
$\Rightarrow B D = C D$
Also, $A B = A C$ and $A D$ is the common side.
$∴$ By S - S - S congruency
$Δ A D B ≅ Δ A D C$ .