Proof for Validation for Construction of a Triangle with Given Perimeter and Two Base Angles

Q. Construct ∆PQR such that, m$\angle$P = 80^°, m$\angle$Q = 70^°, l(QR) = 5.7 cm.

Q.

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:

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

$\text{2. Make}\angle LXY\text{equal to}\angle B\text{and}\angle MYX\text{equal to}\angle C.$

$\text{3. Bisect}\angle LXY\text{and}\angle MYX.\text{Let these}\text{bisectors intersect each other at A.}$

$\text{4. Draw perpendicular bisectors DE of AX}\text{and FG of AY.}$

$\text{5. Let BQ intersect XY at B and RC}\text{intersect XY at C. Join AB and AC.}$

$\text{6. The triangle ABC is thus formed.}$

$\text{How many isosceles triangles are there}\text{in this figure?}$

1. 0
2. 1
3. 2
4. 4

Q.

Which of the following properties/methods is not used in the construction method of Triangle Construction 3?

1. Exterior angle of triangle

2. Isoceles triangle

3. None of these

4. Perpendicular bisector