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?

Cut a line segment BD equal to (AB+AC) on that same ray

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Change the base length to (AB+AC) and then draw one of the base angles at one of the ends of the line segment whose length is equal to (AB+AC)

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He knows the perimeter of the triangle, he changes the base length to that of the perimeter of the triangle and then draws one of the base angles at one of the ends of the line segment

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Cut a line segment BD equal to $2 (A B + A C)$ on that same ray

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Solution

The correct option is A
Cut a line segment BD equal to (AB+AC) on that same ray

We have been given the base length and a base angle, which means half the job is already done for us.

We need to draw the base with the given length and draw a ray with an angle = base angle, after that we must cut a line segment BD equal to (AB + AC) on that same ray so as to perpendicularly bisect the ray DC and have AD = AC because A is the point where the perpendicular bisector of ray DC cuts BD.

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Similar questions

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?

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.

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?

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:

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?

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