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In Fig. 7.21, AC = AE, AB = AD and ∠BAD = ∠EAC. Show that BC = DE.
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)
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
In the given figure, AC = AE, AB = AD, and ∠BAD = ∠EAC, we have proved that BC = DE because ΔBAC ≅ ΔDAE using SAS congruence.
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