Construction of an Angular Bisector and its Proof

Q.

OX bisects $\angle AOB$. C is any point on OX. If $CD\perp OA$ and $CE\perp OB$, then which of the following is true?

1. $△COD\cong △COE$ by AAS postulate
2. $△COD\cong △COE$ by RHS postulate
3. CO = DO = EO
4. $△COD\cong △COE$ by ASA postulate

Q.

In $\Delta$ABC, AB = AC and the bisectors of angles B and C intersect at point O. Prove that BO = CO and the ray AO is the bisector of angle BAC.
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Q. The bisector of an angle lies

1. Any where in the plane
2. On the arms of the angle
3. To the exterior of the angle
4. To the interior of the angle

Q. If a wheel has six spokes equally spaced, then find the measure of the angle between two adjacent spokes.

Q.

Is it possible to construct an angle of 135° with the help of compass and ruler? State with true or false.

1. False

2. True

Q. In the construction of $\angle {135}^{\circ }$ , how many arcs are drawn?

1. 2
2. 4
3. 6
4. 8

Q. In the given figure, OE = OD. Which of the following are true?

1. OX is angle bisector $\angle AOB$
2. C is the midpoint of OX
3. $\angle AOX=\angle AOB$
4. $2\angle AOX=\angle AOB$

Q.
$\text{In the figure,}△ABC\text{is an equilateral}\text{triangle with each side measuring 6 cm. If AD bisects}\angle BAC,\text{then what is the value of BD}\text{in cm?}$

1. 3

Q. Which congruency rule is used to prove the construction of an angular bisector.

1. SSS
2. SAS
3. ASS
4. RHS

Q.

We can construct a ${60}^{\circ }$ angle with a compass and ruler.

1. ruler

2. compass

Q.

ABCD is a trapezium, AB II DC. If ∠A = ∠B = 40^o the measure of the other two angles is

1. 140^o, 140^o

2. 50^o, 50^o

3. 100^o, 100^o

4. 60^o, 60^o

Q.

It is given that ∠XYZ = and XY is produced to point P. Draw a figure from the given information. If ray YQ bisects ∠ZYP, find ∠XYQ and reflex ∠QYP.

Q. How many angler bisectors are drawn to construct an angle of ${22.5}^{\circ }$

1. 1
2. 2
3. 3
4. 4

Q.

Which angle has a large measure? First estimate and then measure.

Measure of angle A =

Measure of angle B =

Q.

Find the measure of an angle of 37degree 42'34".

Q. Construct 🔺 ABC in which BC = 6 CM, angle A = 30 and AC-AB = 3 CM.

Q.

Bisector of an angle divides the angle into

1. Three parts

2. Two parts

3. Two equal parts

4. Four parts

Q. in a quadriletral ABCD the line segment bisect\angle C and\angle D meet atE prove that \angle A+\angle B =2\angle CE

Q.

A ${40}^{\circ }$ angle can be drawn by drawing an angle bisector of a given ${80}^{\circ }$ angle.

1. True

2. False

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

1. 
2. 
3. 
4. 

Q.

For construction of a ${60}^{\circ }$ angle, which of the following instruments is not necessary.

1. compass

2. ruler

3. protractor

4. none of these

Q.

Is it possible to construct an angle of 52.5${}^{\circ }$ with the help of compass and ruler? State with true or false.

1. False

2. True