Question

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Answer 1

Answer:

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Answer 2

Answer:

Step-by-step explanation:

To prove: a) BD = CE     b) AD = AE

Sol: If we can somehow prove that △ABD ≅ △ACE then the above two proves can be done by using CPCT.

       AB = AC (given)

=>   <ABC = <ACB (Angles opp. to equal sides are equal) -(1)

      <DBC = <ECB = 90° (given)

=>   <DBA + <ABC = <ECA + <ACB = 90°

=>   <DBA = <ECA (using eqn 1) -(2)

Now, we've got an angle and a side for congruency. And only require a third element to prove the same.

<DAB = <EAC (Vertically opp. angles) -(3)

Now, using Eq. (1), (2), (3),

                              △ABD ≅ △ACE (by S.A.S rule)

i) BD = CE (by C.P.C.T)

ii) AD = AE (by C.P.C.T)