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Construction of a Triangle ABC with Given Base, Base Angle and Difference between Two Sides AB & AC, with AB >AC

Pavan asked P...

Question

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.

1,2,3,4

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1,4,3,2

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1,4,2,3

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1,3,2,4

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Solution

The correct option is D 1,3,2,4
Correct steps of construction
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 from ray BX.
3. Join DC and draw the perpendicular bisector, say PQ of DC.
4. Let it intersect BX at a point A. Join AC

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Similar questions

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:

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?

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?

Pinku was a hard working student who used to learn without understanding. He was asked to construct a triangle say ABC and was given the base length of the triangle BC, one of the base angles say $∠$ B and the sum of the other two sides (AB + AC). He went about constructing the triangle in the following way:

He drew the base BC with the given dimension, drew the $∠$ B along the ray BX with the angle known to him already. He then took B as centre and (AB + AC) as radius and cuts an arc on the ray BX intersecting the ray at D.

He then joins D to C. He then draws a perpendicular bisector of the line DC and the perpendicular bisector intersecting on the ray intersects the ray at point A. The teacher then asked him as to why he did what he did, she started from the back and asked him as to how the intersection of the ray and the perpendicular bisector gives A.

Which of the following is the reason for him drawing the perpendicular bisector and intersecting it with the ray?

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