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Standard IX

Mathematics

SSS Criteria for Congruency

Given that qu...

Question

Given that quadrilateral ACBD is a kite. By which congruency property are the triangles ACB and ADB congruent?

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Solution

In $△ A B C$ and $△ A B D$ ,
AC = AD (Given)
CB = DB (Given)
AB is the common side.
$⟹ △ A B C ≅ △ A B D$ by SSS congruency rule.

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Similar questions

Given below are pairs of congruent triangles. State the property of congruence and name the congruent triangles in each case.
(i)

(ii)

(iii)

(iv)

(v)

Q. Given that

□ A C B D

is a kite. By which congruence criterion are the triangles

A C B

and

A D B

congruent?

Q. In quadrilateral

A C B D, A B

is a diagonal. If

A C = A D

and

A B

bisects

∠ A

, by which congruence property is

△ A C B ≃ △ A D B

Q. Given that ACBD is a kite.

Assertion: The triangles ACB and ADB are congruent.
Reason: SSS congruence rule is used to prove that these triangles are congruent.

Q. In the quadrilateral ACBD, AB is a diagonal. If AC = AD and AB bisects

∠ A

, by which congruence property is

Δ A C B ≅ Δ A D B

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Given that quadrilateral ACBD is a kite. By which congruency property are the triangles ACB and ADB congruent?

In △ABC and △ABD, AC = AD (Given) CB = DB (Given) AB is the common side. ⟹△ABC≅△ABD by SSS congruency rule.

In $△ A B C$ and $△ A B D$ ,
AC = AD (Given)
CB = DB (Given)
AB is the common side.
$⟹ △ A B C ≅ △ A B D$ by SSS congruency rule.