In Fig. 7.21, AC = AE, AB = AD and ∠BAD = ∠EAC. Show that BC = DE.

Solution:

Given: AC = AE, AB = AD and ∠BAD = ∠EAC

To Prove: BC = DE

We can show two triangles BAC and DAE are congruent triangles by using SAS congruency rule and then we can say corresponding parts of congruent triangles will be equal. 

It is given that ∠BAD = ∠EAC

Thus, by adding ∠DAC to both sides of this equation, we get 

∠BAD + ∠DAC = ∠EAC + ∠DAC (∠DAC is common)

∠BAC = ∠DAE

In ΔBAC and ΔDAE,

AB = AD (Given)

∠BAC = ∠DAE (Proven above)

AC = AE (Given)

∴ ΔBAC ≅ ΔDAE (By SAS congruence rule)

∴ BC = DE (By CPCT)

☛ Check: NCERT Solutions for Class 9 Maths Chapter 7

Video Solution:

In Fig. 7.21, AC = AE, AB = AD and ∠BAD = ∠EAC. Show that BC = DE

NCERT Maths Solutions Class 9 Chapter 7 Exercise 7.1 Question 6

Summary:

In the given figure, AC = AE, AB = AD, and ∠BAD = ∠EAC, we have proved that BC = DE because ΔBAC ≅ ΔDAE using SAS congruence.

☛ Related Questions:

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