# In quadrilateral ACBD, AC = AD and AB bisects ∠A (see Fig. 7.16). Show that Δ ABC ≅ Δ ABD. What can you say about BC and BD?

**Solution:**

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.

**Video Solution:**

## In quadrilateral ACBD, AC = AD and AB bisects ∠A (see Fig. 7.16). Show that Δ ABC ≅ Δ ABD. What can you say about BC and BD?

### NCERT Maths Solutions Class 9 - Chapter 7 Exercise 7.1 Question 1:

**Summary:**

If in quadrilateral ACBD, AC = AD, and AB bisects ∠A, we see that Δ ABC ≅ Δ ABD using SAS congruence and hence, BC and BD are of equal lengths by CPCT.