Students can go through AP Board 7th Class Maths Notes 10th Lesson Construction of Triangles to understand and remember the concept easily.

## AP Board 7th Class Maths Notes 10th Lesson Construction of Triangles

→ The triangles can be constructed given the following cases :

- Three sides of a triangle.
- The lengths of any two sides and the measure of the angle between these sides.
- The measures of two angles and the lengths of side included between them.

→ To Construct a triangle we need at least the measure of one side.

Construct a triangle ABC given that AB = 4 cm, BC = 6 cm and AC = 5 cm.

Steps of construction:

- Draw a line segment BC = 6 cm.
- With B as centre and radius 4 cm, draw an arc.
- With C as centre and radius 5 cm, draw another arc, cutting the previous arc atA.
- Join BA and CA.
- ∆ABC is formed.

→ Construction of a triangle given two sides and an included angle.

Construct triangle PQR given that PQ = 4cm,QR = 6.5cm and ∠Q = 60°.

Steps of construction:

- Draw a line segment QR = 6.5 cm.
- Using a protractor, draw ∠PQR = 60°.
- With Q as centre and radius 4 cm, draw an arc, cutting the ray \(\overrightarrow{\mathrm{QX}}\) at P
- Join RP
- ∆PQR is formed.

→ Construction of a right angled triangle given a base and hypotenuse.

Construct a right angled triangle ABC given that AB = 4 cm, ∠A = 90°, AC = 3 cm.

For making angle 90:

- Take A as center and with any radius, draw an arc intersecting AB at O.
- Now O as center and same radius as before, draw an arc intersecting previous arc at P.
- Now P as center and same radius as before, draw an arc intersecting previous arc at Q.

Steps of Construction:

- Draw a line segment AB = 4 cm. .
- At A, draw an angle of 90° and name the line as AX;
- With A as centre and radius 3 cm, draw an arc cutting the line AX at C.
- Join BC.
- ∆ABC is formed.

→ Construction of a triangle given two angles and a side included between them.

Construct a triangle XYZ in which ∠X = 30°, ∠Y = 100° and XY = 6 cm.

Steps of Construction:

- Draw a line segment XY of length 6 cm.
- Using a protractor, draw ∠YXP = 30° at point X.
- Again using the protractor, draw ∠XYQ = 100° at point Q, intersecting the ray PX at Z.
- ∆XYZ is formed.

→ Counting of Triangles