# Construction of an Angular Bisector and its Proof

## Trending Questions

**Q.**What does it mean to have diagonals bisect each other?

- That goes across each other
- The point where diagonals meet is the midpoint
- The angles are congruent
- The full diagonal line is congruent to the other diagonal line

**Q.**

An angle is 24 less than its compliment, then the measure of angle is

**Q.**Question 1

With the help of a ruler and a compass it is not possible to construct an angle of

(A) 37.5∘

(B) 40∘

(C) 22.5∘

(D) 67.5∘

**Q.**

In the figure ABCD is a square. A line segment DX cuts the side BC at X and the diagonal AC at O such that ∠COD = 105^{o} and ∠OXC = y. Then y is equal to

45

^{o}90

^{o}50

^{o}60

^{o}

**Q.**

If 60^{o} angle is bisected twice then what will be measure of each angle that is constructed?

30

^{o}15

^{o}45

^{o}5

^{o}

**Q.**How many triangles can drawn having its angles as 50 degree, 60 degree, 70 degree

**Q.**

In the given figure, the value of x will be

120

50

30

90

**Q.**

OX bisects ∠AOB. C is any point on OX. If CD⊥OA and CE⊥OB, then which of the following is true?

- △COD≅△COE by AAS postulate
- △COD≅△COE by RHS postulate
- CO = DO = EO
- △COD≅△COE by ASA postulate

**Q.**

In ΔABC, 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.

[4 MARKS]

**Q.**The bisector of an angle lies

- Any where in the plane
- On the arms of the angle
- To the exterior of the angle
- 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.

False

True

**Q.**In the construction of ∠ 135∘ , how many arcs are drawn?

- 2
- 4
- 6
- 8

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

- OX is angle bisector ∠AOB
- C is the midpoint of OX
- ∠AOX=∠AOB
- 2∠AOX=∠AOB

**Q.**

In the figure, △ABC is an equilateral triangle with each side measuring 6 cm. If AD bisects ∠BAC, then what is the value of BD in cm?

- 3

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

- SSS
- SAS
- ASS
- RHS

**Q.**

We can construct a 60∘ angle with a compass and ruler.

ruler

compass

**Q.**

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

140

^{o}, 140^{o}50

^{o}, 50^{o}100

^{o}, 100^{o}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∘

- 1
- 2
- 3
- 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

Three parts

Two parts

Two equal parts

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∘ angle can be drawn by drawing an angle bisector of a given 80∘ angle.

True

False

**Q.**Observe the given construction, if ∠BAE=60∘, then ∠BAC will be:

**Q.**

For construction of a 60∘ angle, which of the following instruments is not necessary.

compass

ruler

protractor

none of these

**Q.**

Is it possible to construct an angle of 52.5∘ with the help of compass and ruler? State with true or false.

False

True