Question

In figure, AD = AE and D and E are points on
BC such that BD = EC. Prove that AB = AC.​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

$\huge\mathfrak{Answer}$

Your question be like

D and E are the points on the base BC of triangle ABC such that AD = AE and triangle BAD = Triangle CAE.

prove that AB = AC

Answer

In $\angle$ABC

AD = AE

$\angle$ADE = $\angle$AED (angle opp. equal sides are equal)

$\angle$ADC = $\angle$AED (same angle)

$\angle$BAD = $\angle$CAE

Adding $\angle$DAC on both sides we get $\angle$BAD + $\angle$DAE = $\angle$CAE + $\angle$DAE

$\angle$BAE = $\angle$CAD

In $\triangle$BAE and $\triangle$CAD

$\angle$AEB = $\angle$ADC

AE = AD (given)

$\angle$BAE = $\angle$CAD (proved)

$\triangle$BAE = $\triangle$CAD (ASA Congruence)

AB = AC ( c.p.c.t) proved

#Answerwithquality

#BAL