ABCD is a trapezium in which AB || CD and AD = BC (see the given figure). From the figure, which of the following can be deduced?

Δ A B C ≅ Δ B C D

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Δ A B C ≅ Δ B C E

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Δ A B C ≅ Δ B A D

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Solution

The correct option is C $Δ A B C ≅ Δ B A D$
In $Δ A B C$ and $Δ A B D$ ,
AB = BA (Common side)
BC = AD (Given)
$∠ B = ∠ A$ (Proved before)
$Δ A B C ≅ Δ B A D$ (SAS congruence rule)

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Question 2
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ABCD is a trapezium in which AB || CD and AD = BC (see the given figure). From the figure, which of the following can be deduced?

The correct option is C ΔABC≅ΔBADIn ΔABC and ΔABD, AB = BA (Common side) BC = AD (Given) ∠B=∠A (Proved before) ΔABC≅ΔBAD (SAS congruence rule)

The correct option is C $Δ A B C ≅ Δ B A D$
In $Δ A B C$ and $Δ A B D$ ,
AB = BA (Common side)
BC = AD (Given)
$∠ B = ∠ A$ (Proved before)
$Δ A B C ≅ Δ B A D$ (SAS congruence rule)