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.