Question

13) Draw a line segment PR equal to 6 cm. Construct
a perpendicular bisector to PR, intersecting PR at
O. On this bisector on either side of PR, mark
points Q and S, such that OQ = OS = 3 cm. Join
PQ, QR, RS and SP. What kind of a figure is
PORS?​

Answer 1

Answer:

(1) 5.3 cm

Steps of construction:

1. Draw line segment AB = 5.3 cm.

2. With A as centre and radius more than half of AB, mark two arcs, one above and other below the line AB.

3. With B as centre and same radius, draw two arcs cutting the previous drawn arcs and name the point of intersection as X and Y.

4. Join XY and name the point where this line cuts AB as point P.  

XY is the perpendicular bisector of AB.  

(2) 6.7 cm

Steps of construction:

1. Draw line segment CD = 6.7 cm.

2. With C as centre and radius more than half of CD, mark two arcs, one above and other below the line CD.

3. With D as centre and same radius, draw two arcs cutting the previous drawn arcs and name the point of intersection as A and B.

4. Join AB and name the point where this line cuts CD as point Q.  

AB is the perpendicular bisector of CD.  

(3) 3.8 cm

Steps of construction:

1. Draw line segment XY = 3.8 cm.

2. With X as centre and radius more than half of XY, mark two arcs, one above and other below the line XY.

3. With Y as centre and same radius, draw two arcs cutting the previous drawn arcs and name the point of intersection as A and B.

4. Join AB and name the point where this line cuts XY as point R.  

AB is the perpendicular bisector of XY.  

Page No 2:

Question 2:

Draw angles of the measures given below and draw their bisectors.

 

(1) 105° (2) 55°  (3) 90°

ANSWER:

(1) 105°

Steps of Construction:

1. Draw a ray BC.

2. With B as centre, use a protractor to make an angle of 105°. Thus, ∠ABC = 105°.  

3. With X and Y as centre, draw arcs intersecting each other at point M.  

BM is the required angle bisector of ∠ABC.

(2) 55°

Steps of Construction:

1. Draw a ray OX.

2. With O as centre, use a protractor to make an angle of 55°. Thus, ∠YOX = 55°.  

3. With P and Q as centre, draw arcs intersecting each other at point A.  

OA is the required angle bisector of ∠YOX.

(3) 90°

Steps of Construction:

1. Draw a ray OB.

2. With O as centre, use a protractor to make an angle of 90°. Thus, ∠AOB = 90°.  

3. With X and Y as centre, draw arcs intersecting each other at point S.  

OS is the required angle bisector of ∠AOB.

Step-by-step explanation: