Chapter 11: Constructions

According to the question,

We have to construct a triangle if its perimeter is 10.4 cm and two angles are 45° and 120°

Steps of construction:

1. Draw XY = 10.4 cm.

2. Draw ∠LXY = 45^o and ∠MYX =120^o

3. Draw the angle bisector of ∠LXY.

4. Draw the angle bisector of ∠MYX such that it meets the angle bisector of ∠LXY at point A.

5. Draw the perpendicular bisector of AX such that it meets XY at B.

6. Draw the perpendicular bisector of AY such that it meets XY at C.

7. Join AB and AC.

Thus, ABC is the required triangle.

According to the question,

We have to draw a triangle PQR such that QR = 3cm, ∠ PQR = 45° and QP – PR = 2 cm

Steps of construction:

1. Draw a ray OX and cut off a line segment QR = 3 cm.

2. AT Q, construction ∠YQR = 45^o.

3. From QY, cut off QS = 2 cm.

4. Join RS.

5. Draw a perpendicular bisector of RS to Meet QY at P.

6. Join PR. Then PQR is the required triangle.