Question

In the adjacent figure if AB = AC and AD is bisector of angleBAC then prove that
(i) triangle ABD=triangle ACD
(ii) angleABD = angleACD
(iii) BD = CD
(iv) triangle DBC is an isosceles triangle
✨Please answer briefly ✨ ​

Answer 1

Answer:

i) To prove ∆ABD≈∆ACD

a) AB=AC (given) isosceles (S)

b) angle BAD= angle CAD (AD is the bisector of BAC) (A)

c) AD=AD(common side) (S)

therefore by S.A.S congruence

∆ABD≈∆ACD (1)

ii) To angle ABD= angle ACD

We know

∆ABD≈∆ACD from (1)

there by C.P.CT(corresponding parts of a congruent triangle)

angle ABD= angle ACD

iii) To prove BD=CD

We know

∆ABD≈∆ACD from (1)

there by C.P.CT(corresponding parts of a congruent triangle)

BD=CD

iv) ∆DBC is an isosceles,

that is we've to prove

BD=CD

or

BC=CD

or

BD=BC

we know

BD=CD from (1) Corresponding parts of a congruent triangle

therefore∆DBC is isosceles

as 2 of its sides are equal

hope it helps