Question

in triangle PQR and triangle ABC, angle B=angle P=90 degrees if AC=QR and PR=BC then prove that the given triangles are congruent

Answer 1

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Answer 2

Solution :-

As we have given that, ∠B = ∠P = 90° .

So, ∆PQR and ∆ABC are right angle ∆'s right angle at B and P .

Than ,

• AB and QP = Let, Perpendicular Length of Both right angle ∆'s.
• PR and BC = Base of both right angle ∆'s.
• Side opposite to right angle of a ∆ is its Hypotenuse , So, QR and AC are Hypotenuse of both right angle ∆'s.

Now, in Right ∆QPR and Right ∆ABC , we have ,

→ ∠QPR = ∠ABC . (Given 90°.)

→ PR = BC . (Given.)

→ QR = AC. (Given. )

using :-

• In two right-angled ∆'s, if the length of the hypotenuse and one side of one triangle, is equal to the length of the hypotenuse and corresponding side of the other triangle, then the two triangles are congruent by RHS Congruence Rule.

Therefore,

→ ∆QPR ≅ ∆ABC . (By RHS congruent.)