Question

In Quadrilateral ABCD AB=CD,BC=AD.Show that ∆ABC is congruent to ∆CDA

Answer 1

Given that :-

• Quadrilateral ABCD . in which
• AB = CD
• BC = AD .

Show that :-

★ ∆ABC ≅ ∆CDA

Construction :-

★ join A to C .

Proof :-

In triangle ABC and CDA

AB = CD (given)

BC = AD (given)

AC = AC (common)

therefore,

∆ABC ≅ ∆CDA

(by SSS criteria)

hence proved ✓✓

criteria for congruence of triangle :-

1. SSS :- side, side ,side :- two triangles are congruence when all side of one triangle is equal to the another triangle.
2. AAA :- angle, angle, angle :- two triangles are congruence when all angles of one triangle is equal to the another triangle.
3. SAS :- side, angle ,side :- two triangles are congruence when two sides and angle between them are equal to another triangle .
4. AAS :- angle, angle, side :- two triangles are congruence when two angles and the side, at which both angles are situated, are equal to the another triangle.
5. RHS :- right angle , hypotenuse, side :- two triangles are congruence when a triangle is right angled . and their hypotenuse and anyone side is equal to the another triangle.

Answer 2

$\sf{\gray{\underbrace{\red{GIVEN:}}}}$

$\implies$$AB = CD$

$\implies$$BC = AD$

$\sf{\gray{\underbrace{\red{TO\:PROVE:}}}}$

$\implies$$ABC = CDA$

$\sf{\gray{\underbrace{\red{SOLUTION:}}}}$

$\implies$$AB = CD$

$\implies$$BC = AD$

$\implies$$AC = AC$

$\sf{Hence \:, ABC\: is \:congruent \:to \:CDA\:}$