Question

in fig .8.73 , AD=BC , AC=BD. Prove that PAB is an isosceles triangle

Answer 1

Hey there !

Solution:

Proof:

Consider Δ DAB and Δ CAB

AD = BD ( S ) ( Given )

AC = BD ( S ) ( Given )

AB = AB ( S ) ( Common )

By SSS Congruence rule,

Δ DAB ≅ Δ CAB

By CPCT, ∠ CAB = ∠ DBA

We know that if there are two equal angles opposite to each other in a same triangle, then theri opposite sides are also equal.

∵ ∠ PBA = ∠ PAB , We can say that, PA = PB .

Since two sides of a triangle are equal we can say that, PAB is an isoceles triangle.

Hope my answer helped !

Answer 2

Answer:

how this helps you friend