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Question :-

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In quadrilateral ABCD, AB = AD and BC = CD. Show that Angle ABC = Angle ADC. ​

Answer 1

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Answer:

TO PROVE :-

∠ABC = ∠ABC

GIVEN THAT:-

• BC = CD

• AB = AD

CONCEPT BEING USED :-

• Congruency of triangles

(We're talking about triangles, from where does this triangle makes its way in?)

Yeah! so let's start this question by dividing the quadrilateral ABCD into two triangles ADC and ABC , by constructing diagonal AC and using it as a common side to both the triangles.

Checking for congruency in these triangles :-

• BC = CD (given)

• AB = AD (given)

• AC = AC (common)

Seeing this, The triangles fall under the category SSS (side side side) under which

" If all the three sides of one triangle are equal to the three corresponding sides of another triangle, the two triangles are congruent."

therefore,

∆ ABC ≡ ∆ ADC

And if two triangles are congruent all their corresponding sides and angles are congruent. (equal) .

and since,

∠ABC and ∠ABC are angles of these triangles they'll be equal

∠ABC = ∠ABC (c.p.c.t.c.)

( Corresponding parts of congruent triangles are congruent)

Hence, proved

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Hope this helps!