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# A triangle PQR given that QR = 3cm, ∠PQR = 45° and QP - PR = 2 cm. Construct the following and give justification

**Solution:**

It is given that in triangle PQR,

QR = 3cm

∠ PQR = 45°

QP - PR = 2 cm

C lies on __perpendicular bisector__ RS of AY

Steps of Construction

1. Construct the base QR of 3 cm length

2. Construct ∠XQR = 45° at point Q of the base QR

3. Now cut the __line segment__ QS = QP - PR = 2 cm from the ray QX

4. Join SR and construct the perpendicular bisector of SR say AB

5. Let AB intersect QX at the point P

6. Join PR

7. Triangle PQR is the required triangle

Justification:

∠PQR and base QR are drawn

P lies on perpendicular bisector of SR

PS = PR

QS = PQ - PS

QS = PQ - PR

Therefore, the construction is justified.

**✦ Try This: **Construct each of the following and give justification: A triangle PQR given that QR = 4cm, ∠ PQR = 65° and QP - PR = 3 cm.

**☛ Also Check: **NCERT Solutions for Class 9 Maths Chapter 11

**NCERT Exemplar Class 9 Maths Exercise 11.4 Problem 2**

## A triangle PQR given that QR = 3cm, ∠PQR = 45° and QP - PR = 2 cm. Construct the following and give justification

**Summary:**

A triangle PQR given that QR = 3cm, ∠ PQR = 45° and QP - PR = 2 cm is constructed and justified

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