Construction of an Angle Bisector

Q.

Draw an angle ABC = ${60}^{\circ }$. Draw the bisector of it. Also draw a line parallel to BC a distance of 2.5 cm from it.

Let this parallel line meet AB at point P and angle bisector at point P. Measure the length of BP and PQ. Is BP = PQ?

Q.

Draw angle ABC of any suitable measure.

(i) Draw BP, the bisector of angle ABC.

(ii) Draw BR, the bisector of angle PBC and draw BQ, the bisector of angle ABP.

(iii) Are the angles ABQ, QBP, PBR and RBC equal ?

(iv) Are the angles ABR and QBC equal ?

Q. A parallelogram is constructed and named KLMN. LP is perpendicular to KL and ML is the angular bisector of $\angle KLP$. Find the value of $\angle KNM$.

1. ${15}^{\circ }$
2. ${45}^{\circ }$
3. ${30}^{\circ }$
4. ${60}^{\circ }$

Q.

Draw a line segment $PQ=6cm$. Draw a perpendicular to $PQ$ at any point on $PQ$. On this perpendicular choose a point $R$ which is $4cm$ away from $PQ$. Through $P$ draw a line $AB$ parallel to $PQ$.

Q.

Draw a line segment of length $6.5cm.$ Draw another line parallel to it at a distance of $4.2cm$ from it.

Q. A 40° angle is obtained by drawing an angle bisector for a given 80° angle.

1. True
2. False
3. Cannot be determined
4. None of the above

Q.

Refer to the following figure:

D and C are equidistant from O.

If any point P is located such that $△$ ODP is congurent to $△$ OCP, then P lies on the ________.

1. Perpenidicular bisector of ∠DOC

2. Altitude of ΔDOC to side DC.

3. Angular bisector of ∠DOC

4. None of these

Q. In which of the following situations an angle bisector cannot be constructed to bisect the angle formed between two given lines?

1. Two intersecting lines
2. Two parallel lines
3. Two perpendicular lines
4. None of the above

Q. A line can be viewed as a circle with infinite radius length.

1. True
2. False

Q.

Observe the given construction, if $\angle BAE={60}^{\circ }$, then $\angle BAC$ will be

1. 
2. 
3. 
4. 

Q.

A parallelogram is constructed and named KLMN. LP is perpendicular to KL and ML is the angular bisector of $\angle KLP$. Find the value of $\angle KLM$.

1. ${15}^{\circ }$

2. ${30}^{\circ }$

3. ${60}^{\circ }$

4. ${45}^{\circ }$

Q.

Which of the following geometrical figure would help you go ahead and draw angles without using protractors?

1. Line

2. Perpenidcular bisector

3. Arcs (part of a circle)

4. None of these

Q.

In which of the following quadrilaterals, a diagonal is not an angle bisector?

1. Square
2. Rectangle
3. Rhombus
4. Parallelogram