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Standard VII

Mathematics

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

The steps to ...

Question

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:

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 A
1,2,3,4

The next step is:
4. Let PQ intersect BX at a point A. Join AC. $Δ$ ABC is the required triangle. The construction is shown in the image below.

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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:

Q. 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.

Q. To construct a

Δ A B C

in which BC = 5.7 cm,

∠ B = 60^{\circ}

and AB - AC = 3cm, the steps of construction are given below.

Here, AB > AC, i.e. the side containing the base angle B is greater than third side
Steps of construction:
Step 1: Draw the base BC = 5.7 cm and draw a ray BY making an

∠ Y B C = 60^{\circ}

Step 2: Cut the line segment BD = 3 cm from the ray BY.
Step 3 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?

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The correct option is A 1,2,3,4 The next step is: 4. Let PQ intersect BX at a point A. Join AC. Δ ABC is the required triangle. The construction is shown in the image below.

The correct option is A
1,2,3,4

The next step is:
4. Let PQ intersect BX at a point A. Join AC. $Δ$ ABC is the required triangle. The construction is shown in the image below.