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

Q.

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

1. Exterior angle of triangle

2. Perpendicular bisector

3. None of these

4. Isoceles triangle

Q.

How many traigles can be draw having its as 30°, 60°and 90°

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. 2
2. 4
3. 1
4. 0

Q.

What is the type of triangle that is created when a ${60}^{\circ }$ angle construction alone is used?__

Q.

A triangle ABC has base angle ${45}^{\circ }$. It's perimeter is $[2+\sqrt{2}]$. What type of triangle is it?

1. Right triangle

2. Scalene triangle

3. Isosceles triangle

4. Can't be determined

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. Construct a ΔABC in which BC = 4.5 cm, ∠C = 45° and sum of sides AB and AC is 8 cm. Justify your construction.

Q. Is it possible to construct a ∆ABC in which BC = 5 cm, ∠B = 60°, ∠C = 60°?
(a) Yes
(b) No

Q.

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

1. Only exterior angle of triangle

2. Only perpendicular bisector

3. Only isoceles triangle

4. Exterior angle property and isosceles triangle property

Q. Is it possible to construct a ∆ABC in which BC = 5 cm, ∠B = 120° and ∠C = 60°?
(a) Yes
(b) No

Q. Without drawing the triangles write all size pairs of equal measures in each of the following pairs of congruent triangles.
$△ABC\cong △LMN$

Q.

A triangle ABC has base angle ${45}^{\circ }$. It's perimeter is $[2+\sqrt{2}]$. What type of triangle is it?

1. Isosceles triangle

2. Right triangle

3. Can't be determined

4. Scalene triangle