Question

In the given figure, ABCD is a square and triangle EAB is an equilateral triangle. Prove that triangle AED is congruent to triangle BEC​

Answer 1

Answer:

Given

ABCD is a square

ABE is an equilateral triangle

To Prove

∆AED congruent to ∆BEC

Proof

We Know ABCD is a square,

AD = BC(sides of square) [1]

We know ABE is equilateral triangle

so, AE = BE [2]

Angle DAE = DAB - EAB

= 90° - 60°

= 30°

Similarly,

Angle EBC = ABC - ABE

= 90° - 60°

= 30°

Angle DAE = Angle EBC [3]

Now, IN ∆AED and ∆BEC

AD = BC

AE = BE

Angle DAE = Angle EBC

Therefore, By SAS congruency

∆AED is congruent to ∆BEC