Construction of Right Triangles

Q. (a) Construct a right-angled triangle ABC such that side $\overline{BC}=8cm$ and hypotenuse $\overline{AC}=10cm$.

(b) Draw a right-angled triangle at C in which AB = 7 cm and BC = 5 cm. [4 MARKS]

Q.

Construct the triangle XYZ, in which XY = 6 cm ∠X = 60°, ∠Y = 30°. Measure the third angle.

Q.

Construct a triangle ABC in which BC is 6 cm, $\angle$B is ${70}^{\circ }$ and AC - AB = 2. [4 MARKS]

Q. Which of the following measurements of sides is possible to construct a triangle?

1. 2 cm, 3 cm, 4 cm
2. 2 cm, 3 cm, 5 cm
3. 2 cm, 3 cm, 6 cm
4. 3 cm, 4 cm, 5 cm

Q. Which of the triangles whose three sides are given below can be constructed?

(a) 9 m, 5 m, 3 m

(b) 10 cm, 10 cm, 4 cm [4 MARKS]

Q.

Construct a triangle ABC in which BC is 4 cm, $\angle B$ is ${45}^{\circ }$ and AB - AC =1.75 cm. [4 MARKS]

Q.

Ram and Shyam were playing with a ball in the room. They somehow managed to break the window pane. Now, they both peered out of the window (shown in the figure below), and made the following statements:

Ram: The bars in the window make right angle.

Shyam: The bars in the window make acute angle.

1. Ram is correct, Shyam is also correct.

2. Ram is correct, Shyam is incorrect.

3. Ram is incorrect, Shyam is correct.

4. Both are incorrect.

Q.

Construct a triangle ABC in which BC is 3 cm, $\angle$ B is ${60}^{\circ }$ and AC - AB = 1 cm. [3 MARKS]

Q.

$△$ABC is such that AB = 5.5 cm and $\angle$A = 90${}^{\circ }$. Which among the given options is correct if we need to construct $△$ABC?

1. Length of side BC $>$ 5.5 cm

2. Length of side BC $<$ 5 cm

3. Length of side BC $<$ 5.5 cm

4. Length of side BC = 5.5 cm

Q.

The sides of the triangle are 3 m, 5 m and 9 m. Construct a triangle. [2 MARKS]

Q. Find the perimeter of an equilateral triangle with a side measuring 4.25 cm.

1. 8.5 cm
2. 10 cm
3. 12.75 cm
4. 17 cm

Q. Angles on one side of a straight line always add to ___ degrees.

Q.

Construct the triangle MRB in which RB = 5.2 cm. ∠R = 30°, ∠B = 120° and measure ∠M.

Q.

The perimeter of the following triangle is

1. 2.5 cm

2. 5.5 cm

3. 6 cm

4. 6.5 cm

Q.

The perimeter of an equilateral triangle with side 9 mm is

1. 2.7 cm

2. 27 cm

3. 0.027 cm

4. 0.27 cm

Q.

The magnitude of __ is expressed in degrees.

Q.

A right triangle with lengths of perpendicular sides 8 cm and 4 cm is constructed. Then the perimeter of this triangle is

1. 21.8 cm

2. 20.9 cm

3. 16.9 cm

4. 15.8 cm

Q.

A right triangle with the lengths of perpendicular sides 5 cm and 6 cm is constructed. Then, the length of the third side is

1. 7.8 cm

2. 6.6 cm

3. 7.2 cm

4. 8.2 cm

Q. When an angle included is _____, it is a right angled triangle.

1. 90 degree
2. 180 degree
3. 45 degree
4. 120 degree

Q. Draw a right triangle whose hypotenuse is of length 4 cm and one side is of length 2.5 cm.

Q. Is it possible to form a triangle by three lines of segments of the following lengths?
6cm, 6cm, 6cm

Q.

A right triangle with the lengths of perpendicular sides 5 cm and 6 cm is constructed. Then, the length of the third side is

1. 6.6 cm

2. 7.2 cm

3. 7.8 cm

4. 8.2 cm

Q. ________ triangle can be uniquely constructed by knowing two sides and any other angle.

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

Q. When one of the angles of a triangle is ${90}^{\circ }$, it is a right angled triangle.

1. True
2. False

Q. A right triangle with lengths of perpendicular sides 8 cm and 4 cm is constructed. Then find the perimeter of this triangle.

Q.

$△$ABC is such that AB = 5.5 cm and $\angle$A = 90${}^{\circ }$. Which among the given options is correct if we need to construct $△$ABC?

1. Length of side BC $<$ 5.5 cm

2. Length of side BC = 5.5 cm

3. Length of side BC $>$ 5.5 cm

4. Length of side BC $<$ 5 cm

Q. Construct a right-angled triangle one side of which measures 3.5 cm and the length of whose hypotenuse is 6 cm.

Q. For constructing a triangle, we must know two sides and included angle. Which triangle can be uniquely constructed by knowing two sides and any other angle?

1. None of the above
2. Equilateral triangle
3. Right angled triangle
4. Scalene triangle

Q.

For constructing a triangle, we must know two sides and included angle. Which triangle can be uniquely constructed by knowing two sides and any other angle?

1. Equilateral triangle

2. Right angled triangle

3. Isosceles triangle

4. Scalene triangle

Q. Construct a ∆ABC in which AB = 3.8 cm, ∠A = 60° and AC = 5 cm.