Question

In Quadrilateral ACBD, AC = AD and AB bisects A.

Show that the two triangles

are congruent.​

Answer 1

Answer:

Given: AC = AD and AB bisects ∠A

To Prove: Δ ABC ≅ Δ ABD 

We can show two sides and included angle of ABC are equal to the corresponding sides and included angle of ABD.

 

In Δ ABC and Δ ABD,

AC = AD (Given)

∠CAB = ∠DAB (AB bisects ∠A)

AB = AB (Common)

∴ Δ ABC ≅ Δ ABD (By SAS congruence rule)

∴ BC = BD (By CPCT)

Therefore, BC and BD are of equal lengths.

☛ Check: NCERT Solutions for Class 9 Maths