If ∆PQR and ∆SQR are both isosceles triangle on a common base QR such that P and S lie on the same side of QR. Are triangles PSQ and PSR congruent? Which condition do you use?

Solution:

Given, PQR and SQR are isosceles triangles on a common base QR.

P and S lie on the same side of QR.

We have to determine if the triangles PSQ and PSR are congruent.

Considering triangle PSQ and PSR,

Given, PQ = PR

Also, SQ = SR

Since P and S lie on the same side of QR,

Common side = PS

Side-Side-Side congruence rule states that if three sides of one triangle are equal to three corresponding sides of another triangle, then the triangles are congruent.

By SSS rule, ∆PSQ ≅ ∆PSR

✦ Try This: If ∆ABC and ∆DBC are both isosceles triangle on a common base BC such that A and D lie on the same side of BC. Are triangles ADB and ABC congruent? Which condition do you use?

☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 6

NCERT Exemplar Class 7 Maths Chapter 6 Problem 147

If ∆PQR and ∆SQR are both isosceles triangle on a common base QR such that P and S lie on the same side of QR. Are triangles PSQ and PSR congruent? Which condition do you use?

Summary:

If ∆PQR and ∆SQR are both isosceles triangle on a common base QR such that P and S lie on the same side of QR. ∆PSQ ≅ ∆PSR by SSS congruence criterion.

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