Mathematics · Triangles · NCERT Examples
Example 3
A complete, independently verified solution for NCERT Example 3.
Change resourceExample 3
Mathematics · Chapter 6 · NCERT Examples
Verified NCERT questions and solutionsSolutions are checked independently and follow the supplied NCERT chapter edition.
NCERT Example
Example 3
In Figure 6.16, PS/SQ = PT/TR and ∠PST = ∠PRQ. Prove that PQR is an isosceles triangle.
Solution
Given:
S and T lie on PQ and PR, respectively; PS/SQ = PT/TR and angle PST equals angle PRQ.
To prove:
Triangle PQR is isosceles.
Proof:
Since S and T divide PQ and PR in the same ratio, ST ∥ QR by the converse of BPT.
Therefore, ∠PST = ∠PQR because they are corresponding angles.
But ∠PST = ∠PRQ is given. Hence ∠PQR = ∠PRQ.
Sides opposite equal angles of a triangle are equal, so PR = PQ.
Final answer
Therefore, △PQR is isosceles with PQ = PR.