Question

In ΔPQR

Options

• PQ – QR > PR

• PQ > QR

• PR < PQ + QR

• PR > PQ

Answer 1

PR < PQ + QR

Explanation:

To determine the correct relationship in ΔPQR, we rely on the triangle inequality theorem, which states:

The sum of the lengths of any two sides of a triangle must be greater than the third side.

Specifically, for ΔPQR, we must have:

• PQ + QR > PR
• PQ + PR > QR
• PR + QR > PQ

Now check the options:

1. PQ – QR > PR → Not always true, subtraction doesn’t apply in triangle inequality.
2. PQ > QR → Not necessarily true; no information given.
3. PR < PQ + QR → Correct (directly follows from triangle inequality)
4. PR > PQ → Not necessarily true; no basis.