Question

In the given figure ,AD=AB and AE bisects angle prove that BE=ED and angle ABC>angle BCA​

Answer 1

Answer:

given: AD= AB

AE is bisects

to prove: i) BE= ED ii) angle ABC>angle BCA

Proof:

i) In ∆ ABE and ∆ ADE we have,

AB= AD ( given)

angle BAE=angle DAE ( given)

AE= AE( common)

∆ ABE congruent to ∆ ADE (SAS criteria)

BE= ED ( c.p.c.t.).

ii) In ∆ ABD, we have: AB= AD

therefore, angle ABD= angle BDA

but, angle BDA being an exterior angle of ∆ BCD, we have:

angle BDA> angle ACB

thus, from (I) and (ii), we get:

angle ABD > angle ACB

angle ABC > angle ABD

angle ABC > angle ACB.

Hence, angle ABC > angle ACB.

Answer 2

Answer:

This is the answer of the question