Question

in ∆ABC and ∆DEF , ∠A=∠D,∠B=∠E and AB=DE, then are the triangles congruent? If yes, by which congruency rule? *

AAS

ASA

RHS

No they not congruent


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Answer 1

Required Answer -

$\huge{\boxed{\sf{\orange{(ii)ASA}}}}$

Explαnαtion -

As you can clearly see in the image attached the two angles and the included side of ∆ABC are equal to two angles and the included side ∆DEF, therefore this triangles are congruent by ASA(Angle Side Angle) congruency rule.

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Additionαl information :

Congruent - If two shapes have same size and same shape then they will be congruent.

Congruent triangles - If all the angles and sides of a triangle are equal to all the angles and sides of the other traingle, they will be congruent triangles.

In mathematics, it is not necessary to prove all the sides and angles to need a pair of congruent triangles. There are some congruency rules which can use to prove congruent triangles.

There are total five congruency criteria or postulates.

• SSS(Side Side side)
• SAS [Side (included) Angle Side]
• ASA [Angle (included)side Angle]
• AAS [Angle Angle Side]
• RHS ( Right angle Hypotenuse Side) only for right angle triangles!

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Answer 2

$\large\bf{\underline\green{☕︎Good \: Morning☕︎}}$

➜ ASA