Construction of Isosceles Triangle When Its Altitude and Vertex Angle Are Given

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. Isosceles triangle

3. Can't be determined

4. Scalene triangle

Q. Construction of isosceles triangle ABC is given below, where altitude = 4cm and $\angle A={90}^{\circ }$.Then $\Delta ABM$ is a/an:

1. Isosceles triangle
2. Right angled triangle
3. Isosceles rightangle triangle
4. Scalene triangle

Q.

Construct a triangle ABC, in which $\angle$B = ${60}^{\circ }$, $\angle$C = ${60}^{\circ }$ and AB + BC+ CA = 18 cm. What type of triangle is this? Find the length of each side by calculation. Verify the calculation from the construction. [4 MARKS]

Q. Steps for the construction of a isosceles triangle ABC whose altitude is 4cm and vertex angle is ${80}^{\circ }$ is given below. Choose the correct order.

1.With M as centre and radius 4cm, draw an arc cutting MP at A.
2.Construct B and C on XY such that $\angle MAB=\frac{80}{2}={40}^{\circ }$ and $\angle MAC=\frac{80}{2}={40}^{\circ }$
3.Take a point M on point XY, and draw a line MP$\perp$ XY
4.Draw a line segment XY.

1. 4, 3, 2, 1
2. 4, 2, 1, 3
3. 1, 3, 2, 4
4. 4, 3, 1, 2

Q. If Rahul constructed an isosceles $\Delta$ ABC with a ${30}^{\circ }$ vertex angle at B then :

1. AB = BC
   
2. AC = AB
3. AC = AB = BC

Q. Match the values of $x$ for the following, given that triangles ABC are isosceles triangles with AB=AC.

1. ${80}^{\circ }$
2. ${70}^{\circ }$
3. 10cm

Q. Steps for the construction of a isosceles triangle ABC whose altitude is 4cm and vertex angle is ${80}^{\circ }$ is given below. Choose the correct order.

1.With M as centre and radius 4cm, draw an arc cutting MP at A.
2.Construct B and C on XY such that $\angle MAB=\frac{80}{2}={40}^{\circ }$ and $\angle MAC=\frac{80}{2}={40}^{\circ }$
3.Take a point M on point XY, and draw a line MP$\perp$ XY
4.Draw a line segment XY.

1. 4, 3, 2, 1
2. 4, 2, 1, 3
3. 4, 3, 1, 2
4. 1, 3, 2, 4

Q. In $\Delta ABC$, altitude BE= altitude CF. Then triangle ABC is

1. Equilateral triangle
2. Right angled triangle
3. Isosceles triangle
4. Scalene triangle

Q. We can construct an isosceles triangle, if the length of the base and the value of the vertex angle are given.

1. False
2. True

Q. A triangle with one angle ${120}^{\circ }$ and three different sides is:

1. acute angled triangle
2. Scalene obtuse angled triangle
3. Obtuse angled triangle
4. Scalene triangle

Q. The equal angles of an isosceles triangle are ${50}^{\circ }$ each. Then third angle is equal to:

1. ${80}^{\circ }$
2. ${50}^{\circ }$
3. ${60}^{\circ }$
4. ${70}^{\circ }$

Q. The vertex angle of an isoceles triangle is ${100}^{\circ }$ . Find the base angle?

1. ${50}^{\circ }$
2. ${40}^{\circ }$
3. ${60}^{\circ }$
4. ${45}^{\circ }$