Which congruence criterion is used in the following?
Given: EB = BD, AE = CB, $∠ A = ∠ C = 90^{\circ}$

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Solution

In $Δ A E B$ and $Δ C B D$ ,

$E B = B D$ [hypotenuse]

$A E = C B$ [Given]

$∠ A = ∠ C = 90^{\circ}$ [Given]

Hypotenuse and one side of a right-angled triangle are equal to the hypotenuse and one side of another right-angled triangle.

$∴ Δ A B E ≅ Δ C D B$ [RHS congruence criterion]

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∠ A = ∠ C = 90^{\circ}

∠ A = ∠ C = 90^{\circ}

Δ A B E ≅ Δ C D B

Question 1 (d)
Which congruence criterion do you use in the following?
Given: EB = BD, AE = CB, $∠ A = ∠ C = 90^{\circ}$

∠ A = ∠ C = 90^{\circ}

Δ A B E ≅ Δ C D B

∠ A = ∠ C = 90^{\circ}

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