Draw a right triangle ABC in which BC = 12 cm, AB = 5 cm and ∠B = 90°. Construct a triangle similar to it and of scale factor 2/3. Is the new triangle also a right triangle

Solution:

It is given that

In a right triangle ABC

BC = 12 cm, AB = 5 cm and ∠B = 90°

We have to find if the new triangle is a right triangle

Steps of construction:

1. Construct a line segment AB = 5cm. At the point A draw a right triangle SAB

2. Construct an arc of radius 12 cm with B as its centre which intersects SA at the point C.

3. Now join BC to obtain ABC

4. Construct a ray AX which makes an acute angle with AB opposite to the vertex C

5. Let us locate 3 points A₁, A₂, A₃ on the line segment AX where AA₁ = A₁A₂ = A₂A₃.

6. Join A₃B

7. Construct a line through A₂ parallel to A₃B which intersects AB at B’.

8. Construct a line parallel to BC which intersects AC at C’ through B’

9. So triangle AB’C’ is the required triangle.

Therefore, the new triangle is also a right triangle.

✦ Try This: Draw a right triangle ABC in which BC = 10 cm, AB = 4 cm and ∠B = 90°. Construct a triangle similar to it and of scale factor 3/4. Is the new triangle also a right triangle?

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 11

NCERT Exemplar Class 10 Maths Exercise 10.3 Problem 2

Draw a right triangle ABC in which BC = 12 cm, AB = 5 cm and ∠B = 90°. Construct a triangle similar to it and of scale factor 2/3. Is the new triangle also a right triangle

Summary:

A right triangle ABC with BC = 12 cm, AB = 5 cm and ∠B = 90° is drawn. A triangle similar to it and of scale factor 2/3 is drawn. The new triangle is also a right triangle

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