Page 207 - Start Up Mathematics_7

Construction of Triangles
We know that triangles are classified on the basis of their sides and angles.
Some important properties of triangles:

1. The sum of three angles of a triangle is 180°.

2. The exterior angle of a triangle is equal to the sum of interior opposite angles.
3. The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

4. In a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of
the squares of the lengths of the other two sides.

In the chapter on ‘Congruence of Triangles’ we observed that a triangle can be drawn if any one
of the following sets of measurements are given:

(a) Three sides (SSS construction criterion)
(b) Two sides and an included angle (SAS construction criterion)

(c) Two angles and an included side (ASA construction criterion)
(d) The hypotenuse and a side in a right-angled triangle (RHS construction criterion)

Case I: SSS criterion

Construction of a triangle when lengths of three A
sides are given

Let’s construct a triangle ABC in which AB = 5.2 cm, 5.2 cm 7.3 cm
BC = 6.5 cm and CA = 7.3 cm.

Construction: Draw a rough sketch of ∆ ABC and mark B 6.5 cm C
the given dimensions.
A
Steps of Construction:

1. Draw a line segment BC measuring 6.5 cm.
2. Draw an arc of radius 5.2 cm taking B as centre.

3. Draw another arc of radius 7.3 cm taking C as 7.3 cm
centre cutting the previous arc at A. 5.2 cm

4. Join AB and AC.

5. ABC is the required triangle.
B
6.5 cm C
X

Example 3: Construct an equilateral triangle of side 5.5 cm. 5.5 cm 5.5 cm
Solution: Construction: Draw a rough sketch of an equilateral
∆ XYZ and mark the given dimensions.
Y 5.5 cm Z

199