# Practical Geometry

**Exercise 1**

**1. **Draw a line, say AB, take a point C outside it. Through C, draw a line parallel to AB using ruler and compasses only.

**2. ** Draw a line *l. *Draw a perpendicular to *l* at any point on *l*. On this perpendicular choose a point X. 4 cm away from *l*. Through X, draw a line *m* parallel to *l.*

**3. ** Let *l* be a line and P be a point not on *l*. Through P, draw a line *m* parallel to *l*. Now join P to meet Q on *l.* Choose any other point R on *m*. Through R, draw a line parallel to PQ. Let this meet *l* at S. What shape do the two sets of parallel lines enclose?

**Exercise 2**

**4. ** Construct Δ XYZ in which XY = 4.5 cm, YZ = 5 cm and ZX = 6 cm.

**5. ** Construct an equilateral triangle of side 5.5 cm.

**6. ** Draw Δ PQR with PQ = 4 cm, QR = 3.5 cm and PR = 4 cm. What type of triangle is this?

7. Construct Δ ABC such that AB = 2.5 cm, BC = 6 cm and AC = 6.5 cm. Measure ∠ B.

**Exercise 3**

**8. **Construct Δ DEF such that DE = 5 cm, DF = 3 cm and m∠ EDF = 90°.

**9. **Construct an isosceles triangle in which the lengths of each of its equal sides is 6.5 cm and the angle between them is 110°.

**10. ** Construct Δ ABC with BC = 7.5 cm, AC = 5 cm and m∠ C = 60°.

**Exercise 4**

**11. ** Construct Δ ABC, given m∠ A = 60°, m∠ B = 30° and AB = 5.8 cm.

**12. ** Construct Δ PQR if PQ = 5 cm, m∠ PQR = 105° and m∠ QRP = 40°.

**Exercise 5**

**13. **Construct the right angled Δ PQR, where m∠ Q = 90°, QR = 8 cm and PR = 10 cm.

**14. ** Construct a right angled triangle whose hypotenuse is 6 cm long and one the legs is 4 cm long.

**15. ** Construct an isosceles right angled triangle ABC, where m∠ ACB = 90° and AC = 6 cm.

**Exercise 6**

**16. **Below are given the measures of certain sides and angles of triangles. Identify those which cannot be constructed and, say why you cannot construct them. Construct rest of the triangle.