Question

in triangles ABC and PQR, AB = PQ and angle B = angle Q. the two triangles will be congruent by SAS axiom if​

Answer 1

Answer:

In ∆ABC and ∆PQR, AB = PR and ∠A = ∠P. The two triangles will be congruent by SAS axiom if: BC = QR. AC = PQ.

Answer 2

The two triangles will be congruent by SAS axiom if​ BC = QR.

Step-by-step explanation:

Given:

In triangles ABC and PQR.

AB = PQ.

Angle B = angle Q.

Concept Used:

Two shapes are congruent if two shapes have the same shape and size. Also if two shapes are congruent, then the mirror image of one shape is the same as the other shape.

SAS (Side-Angle-Side) Axiom

If any two sides and the angle included between the sides of one triangle are equivalent to the corresponding two sides and the angle between the sides of the second triangle, then the two triangles are called to be congruent by SAS axiom.

To Find:

The two triangles will be congruent by SAS axiom if​.

Solution:

As given,In triangles ABC and PQR, AB = PQ and $\angle B = \angle Q.$

AB = PQ

$\angle B = \angle Q$

To apply SAS axiom for two triangles $\angle ABC\ and\ \angle PQR$  will be congruent the  sides of triangle BC = QR  should be equal also.

AB = PQ   [Given]

BC = QR   [Required]

$\angle B = \angle Q$  [Given]

Hence, triangle ABC and PQR are congruent by S.A.S. congruency.

Thus,the two triangles will be congruent by SAS axiom if​ BC = QR.

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