# Practical Geometry

## Exercise 10.2

**Question 1:** Construct ΔXYZ in which XY = 4.5 cm, YZ = 5 cm and ZX = 6 cm.

**Answer:** Draw a line XY = 4.5 cm.

From point Y, draw an arc with radius = YZ = 5 cm.

From point X, draw an arc with radius = ZX = 6 cm.

The point of intersection of both arcs is point Z.

Join the point Z with points X and Y to get a triangle.

**Question 2:** Construct an equilateral triangle of side 5.5 cm.

**Answer:** Draw a line AB = 5.5 cm.

From points A and B, draw arcs with radii = 5.5 cm.

The point of intersection of both arcs is point C.

Join the point C with A and B to get the required triangle.

**Question 3:** Draw ΔPQR with PQ = 4 cm, QR = 3.5 cm and PR = 4 cm. What type of triangle is this?

**Answer:** Draw a line QR = 3.5 cm.

From points Q and R, draw arcs with radii = PQ = PR = 4 cm.

Join the point of intersection of both arcs with points Q and R to get the required triangle.

This is an isosceles triangle.

**Question 4:** Construct ΔABC such that AB = 2.5 cm, BC = 6 cm and AC = 6.5 cm. Measure ∠B.

**Answer:** Draw a line AB = 2.5 cm.

From point B, draw an arc with radius = BC = 6 cm.

From point A, draw an arc with radius = AC = 6.5 cm.

Join the point of intersection of these arcs to points A and B to get the required triangle.