In the figure given below- if - - - - - - and - - - then-

In ΔABC and ΔADE AB = AD [Given] AC = AE nbsp;[Given] ∠BAD = ∠EAC nbsp;[Given] nbsp; —(i) Adding nbsp;∠DAC on both side of the equation (i), ∠BAC = ∠DA ...

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Byju's Answer

Standard VII

Mathematics

AAS Criteria for Congruency

In the figure...

Question

In the figure given below, if 𝐴𝐶 = 𝐴𝐸, 𝐴𝐵 = 𝐴𝐷, and ∠𝐵𝐴𝐷 = ∠𝐸𝐴𝐶, then:

AB = AE

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AD = AC

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BC = DE

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BD = DE

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Solution

The correct option is C BC = DE
In ΔABC and ΔADE
AB = AD [Given]
AC = AE [Given]
∠BAD = ∠EAC [Given] ---(i)
Adding ∠DAC on both side of the equation (i),
∠BAC = ∠DAE

∴ ΔABC ≅ ΔADE [SAS congruence]
⇒ BC = DE [CPCT]

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In the figure given below, if 𝐴𝐶 = 𝐴𝐸, 𝐴𝐵 = 𝐴𝐷, and ∠𝐵𝐴𝐷 = ∠𝐸𝐴𝐶, then:

The correct option is C BC = DEIn ΔABC and ΔADE AB = AD [Given] AC = AE [Given] ∠BAD = ∠EAC [Given] ---(i) Adding ∠DAC on both side of the equation (i), ∠BAC = ∠DAE ∴ ΔABC ≅ ΔADE [SAS congruence] ⇒ BC = DE [CPCT]

The correct option is C BC = DE
In ΔABC and ΔADE
AB = AD [Given]
AC = AE [Given]
∠BAD = ∠EAC [Given] ---(i)
Adding ∠DAC on both side of the equation (i),
∠BAC = ∠DAE

∴ ΔABC ≅ ΔADE [SAS congruence]
⇒ BC = DE [CPCT]