Question

in an isosceles triangle ABC with AB=AC,D and E are poinys on BC such that BE=CD show thatAD=AE​

Answer 1

Answer:

Step-by-step explanation:

Given :- A triangle ABC in which AB=AC. D and E are points on BC such that BE = CD.

To prove :- AD= AE.

proof :- BE=CD

= BE-DE = CD-DE

= BD = CE

NOW IN TRIANGLE ABD AND TRIANGLE ACE,

AB=AC

ANGLE B = ANGLE C

BD = CE

BY SAS CRITERIA, TRIANGLE ABD CONGRUENT TO TRIANGLE ACE.

BY CPCT, AD = DE

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Answer 2

Answer:

we have to prove that ∆abc is congruent to ∆adc

Step-by-step explanation:

ab=ac (given)

<abe=<acd (as it is an isosceles triangle)

be=cd (given)

thus, ∆abe is congruent to ∆acd by SAS criteria.

ad=ae by CPCT.