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Proof for Validation for Construction of a Triangle with Given Base, Base Angle and Difference between Two Sides

The steps to ...

Question

The steps to construct a triangle with given base angles $∠$ B and $∠$ C and BC + CA + AB, are:.
A. Draw a line segment, say XY equal to BC + CA + AB.
B. Make $∠$ LXY equal to $∠$ B and MYX equal to $∠$ C.
C. Bisect $∠$ LXY and $∠$ MYX. Let these bisectors intersect at a point A.
D. Draw perpendicular bisectors PQ of AX and RS of AY.
E. Let PQ intersect XY at B and RS intersect XY at C. Join AB and AC.

True

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False

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Solution

The correct option is A
True

The procedure is standard construction for the given type of triangle. The image of construction is shown below.

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Similar questions

Pallav got following question in his exam:

Given the base angles, say $∠$ B and $∠$ C and BC + CA + AB, construct triangle ABC.

He followed the following steps for the construction.

1. Draw a line segment, say XY equal to BC + CA + AB.

2. Make $∠$ LXY equal to $∠$ B and $∠$ MYX equal to $∠$ C.

3. Bisect $∠$ LXY and $∠$ MYX. Let these bisectors intersect at a point A

4. Draw perpendicular bisectors PQ of AX and RS of AY.

5. Let PQ intersect XY at B and RS intersect XY at C. Join AB and AC

A student constructed a triangle when the perimeter of the triangle and both the base angles are given. The steps of construction he used are as follows:

$1. Draw a line segment, say XY equal to AB + BC + AC.$

$2. Make ∠ L X Y equal to ∠ B and ∠ M Y X equal to ∠ C .$

$3. Bisect ∠ L X Y and ∠ M Y X . Let these bisectors intersect each other at A.$

$4. Draw perpendicular bisectors DE of AX and FG of AY.$

$5. Let BQ intersect XY at B and RC intersect XY at C. Join AB and AC.$

$6. The triangle ABC is thus formed.$

$How many isosceles triangles are there in this figure?$

A student constructed a triangle with the known conditions to him being the perimeter of the triangle and both the base angles. The steps of construction he used are as follows:

1. Draw a line segment, say XY equal to AB + BC + AC

2. Make angles LXY equal to $∠$ B and MYX equal to $∠$ C

3. Bisect $∠$ LXY and $∠$ MXY. Let these bisectors intersect each other at A.

4. Draw perpendicular bisectors PQ of AX and RS of AY

5. Let PQ intersect XY at B and RS intersect XY at C. Join AB and AC.

6. The triangle ABC is thus formed.

How many isosceles triangles are there in this figure?

A student constructed a triangle with the known conditions to him being the perimeter of the triangle and both the base angles. The steps of construction he used are as follows:

1. Draw a line segment, say XY equal to AB + BC + AC

2. Make angles LXY equal to $∠ B$ and angle MYX equal to $∠ C$

3. Bisect $∠ L X Y$ and $∠ M X Y$ . Let these bisectors intersect each other at A.

4. Draw perpendicular bisectors DE of AX and FG of AY

5. Let DE intersect XY at B and FG intersect XY at C. Join AB and AC.