Given are the steps of construction for constructing a triangle ABC whose base length is given say BC, one of the base angles is given, say $∠$ B and the difference between the other two sides is also given (AB – AC) considering AB $>$ AC.

Pinku was asked to give the steps of construction for the same. He had mugged up all the steps of construction but forgot one point in between. Following are those steps of construction, let’s see if you can help Pinku with the missing step.

Steps of construction:

Draw the base BC and at point B make an angle say XBC equal to the given angle. Cut the line segment BD equal to (AB – AC) from ray BX. Let it intersect BX at a point A. Join AC

Which of the following do you think is the missing step of this construction?

Join D to C and draw a perpendicular bisector of the line BC

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Join D to C and draw a perpendicular bisector of the line DC

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Join D to C and draw an angle bisector of the angle B

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Join D to C and draw a perpendicular bisector of the line AC

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B
Join D to C and draw a perpendicular bisector of the line DC

Pinku forgot the most important step of the construction where he has to Join the points D to C and then draw a perpendicular bisector of the line DC and make it intersect with the ray BX. The point of intersection of the perpendicular bisector and the ray gives us the point A, hence we are ready with the triangle ABC.

Why we do this is because if we take into consideration the $△$ AMD and $△$ AMC,

DM = MC (perpendicular bisector)

$∠$ AMD = $∠$ AMC = 90° (perpendicular bisector)

AM = AM (common side)

$△$ AMD $≅$ $△$ AMC (By SAS Congruency)

AD = AC (By CPCT)

This means that its like flipping the point A about the point D such that it merges with the point C.

Suggest Corrections

Similar questions

Given are the steps of construction for constructing a triangle ABC whose base length is given say BC, one of the base angles is given, say $∠$ B and the difference between the other two sides is also given (AB – AC) considering AB $>$ AC.

Pinku was asked to give the steps of construction for the same. He had mugged up all the steps of construction but forgot one point in between. Following are those steps of construction, let’s see if you can help Pinku with the missing step.

Steps of construction:

Draw the base BC and at point B make an angle say XBC equal to the given angle. Cut the line segment BD equal to (AB – AC) from ray BX. Let it intersect BX at a point A. Join AC

Which of the following do you think is the missing step of this construction?

Pavan asked Preeti to draw a triangle. He gave following data

1.the base BC

2.a base angle, say $∠$ B

3.The difference of other two sides AB - AC or AC - AB, Assume, AB $>$ AC

She was unable to draw the triangle ABC. So as a hint he gave steps of construction but it was not in correct order. He gave following steps

1.Draw the base BC and at point B make an angle say XBC equal to the given angle.

2.Join DC and draw the perpendicular bisector, say PQ of DC.

3.Cut the line segment BD equal to AB - AC from ray BX.

4.Let it intersect BX at a point A. Join AC

Arrange the steps in correct order.

A student was given the following details while constructing a triangle ABC:

The length of the base of the triangle BC, one of the base angles say $∠$ B and the sum of the other two sides of the triangle (AB+AC)

He went about the construction of this triangle by first drawing the base of the triangle BC. He then drew an angle at the point B equal to the given angle on a ray that he drew. After completing these steps, he got stuck and doesn’t know what to do next. Which of the following steps will he take up next?

The steps to draw a triangle with the base BC, a base angle $∠$ B and the difference of other two sides is given below.
1. Draw the base BC and at point B make an angle say XBC equal to the given angle.
2. Cut the line segment BD equal to AB - AC on the reflection of ray BX (i.e. BX').
3. Join DC and draw the perpendicular bisector, say PQ of DC.
The next step will be:

A student was given the following details while constructing a triangle ABC:

The length of the base of the triangle BC, one of the base angles say $∠$ B and the sum of the other two sides of the triangle (AB+AC)

Join BYJU'S Learning Program