Question

In figure AB=CD and angles A and D are 90degrees. Prove that the triangles are congruent

Answer 1

Explanation:

In triangle ABC and BDC we have,

AB=CD (Given)

A= D(90° Each)

BC=BC(common)

Therefore,by RHS

Both the triangle s are congruent.

Answer 2

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Given

• AB = AC
• ∠A = ∠D = 90°

To Prove

• △ABC ≅ △CDB

Solution

In △ABC and △CDB

AB = AC [ Given ]

∠A = ∠D [ Given ]

BC = CA [ Common ]

Therefore, △ABC ≅ △CDB by RHS congruence rule.

Additionally

• SSS stands for "side, side, side" and means that we have two triangles with all three sides equal.

• SAS stands for "side, angle, side" and means that we have two triangles where we know two sides and the included angle are equal.

• ASA stands for "angle, side, angle" and means that we have two triangles where we know two angles and the included side are equal.

• AAS stands for "angle, angle, side" and means that we have two triangles where we know two angles and the non-included side are equal.