# Construct a triangle PQR in which QR = 6 cm, Q = ∠60° and PR - PQ = 2 cm

**Solution:**

Steps of Construction:

i) Draw a line QR = 6 cm. Make an angle of 60° at a point RQX using a protractor and extend it below line QR.

ii) With Q as center and radius as 2 cm, draw an arc to intersect the ray QX at Z.

iii) Join RZ.

iv) Construct a perpendicular bisector of ZR. With Z and R as centers and radius greater than half of ZR, draw arcs on either side to intersect each other.

iv) Join the intersecting points and extend them to meet the ray QY at P.

v) Join P and R.

PQR is the required triangle.

Verification:

On measuring we see that,

QR = 6 cm, Q = ∠60° and PR - PQ = 2 cm

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

**Video Solution:**

## Construct a triangle PQR in which QR = 6cm, Q = ∠60° and PR - PQ = 2 cm

Class 9 Maths NCERT Solutions Chapter 11 Exercise 11.2 Question 3

**Summary:**

It is given that we have to construct a triangle PQR in which QR = 6 cm, Q = ∠60°, and PR - PQ = 2 cm. We have drawn the triangle using a compass and ruler and justified the construction.

**☛ Related Questions:**

- Construct an angle of 90° at the initial point of a given ray and justify the construction.
- Construct an angle of 45° at the initial point of a given ray and justify the construction.
- Construct the following angles and verify by measuring them by a protractor:(i) 75°(ii) 105°(iii) 135°
- Construct an equilateral triangle, given its side and justify the construction.

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