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?

Open in App

Solution

Steps of construction :

1. Draw $∠$ ABC = $60^{\circ}$

2. Draw BD, the bisector of $∠$ ABC.

3. Taking B as centre, draw an arc of radius 2.5 cm.

4. Taking C as centre, draw another arc of radius 2.5 cm.

5. Draw a line MN which touches these two arcs drawn.

Then MN is the required line parallel to BC.

6. Let this line MN meets AB at P and bisector BD at Q.

7. Measure BP and PQ.

By measurement we see BP = PQ.

Suggest Corrections

Similar questions

By following these steps of construction,

(i) Draw a line segment PQ = 11 cm

(ii) At P construct an angle of 60^o and at Q, an angle of 45^o.

(iii) Bisect these angles. Let the bisectors of these angles intersect at a point A.

(iv) Draw perpendicular bisectors DE of AP to intersect PQ at B and FG of AQ to intersect PQ at C.

(v). Join AB and AC. Triangle ABC has been obtained. In this ∆ABC,

Q. Draw two parallel lines l and m. Draw three angles 60°, 90° and 120° on one line at points A, P and R which meets another line at points B, Q and S respectively. Measure the length of AB, PQ, and RS. Which is the shortest distance between l and m.
Dis you observe something?

Q. By following these steps of construction,

(i) Draw a line segment PQ = 11 cm

(ii) At P construct an angle of 60^o and at Q, an angle of 45^o.

(iii) Bisect these angles. Let the bisectors of these angles intersect at a point A.

(iv) Draw perpendicular bisectors DE of AP to intersect PQ at B and FG of AQ to intersect PQ at C.

(v). Join AB and AC. Triangle ABC has been obtained. In this ∆ABC,

Q. Construct a parallelogram ABCD, in which AB= 6cm , AD= 3cm and ∠DAB =

60^{\circ}

.
Draw a bisector to angle DAB, let it meet DC at point P. Measure angle APB.

Q. Draw an equilateral triangle. Draw angle bisector of angle A .Let it meet the side BC at D.
Measure the Length BD and CD. Then:

Join BYJU'S Learning Program

Draw an angle ABC = 60∘. 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?

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?