To construct a triangle similar to a given ∆ABC with its sides 7/3 of the corresponding sides of ∆ABC, draw a ray BX making acute angle with BC and X lies on the opposite side of A with respect to BC. The points B₁ , B₂ , ...., B₇ are located at equal distances on BX, B₃ is joined to C and then a line segment B₆C' is drawn parallel to B₃C where C' lies on BC produced. Finally, line segment A'C' is drawn parallel to AC. Write ‘True’ or ‘False’ and justify your answer

Solution:

Steps of construction:

1. Construct a line segment BC.

2. Taking B and C as centers, construct two arcs of suitable radius which intersects each other at A.

3. Now join BA and CA. ∆ABC is the required triangle.

4. From point B, construct a ray BX downwards which makes an acute angle CBX.

5. On BX, mark 7 points, B₁, B₂, B₃, B₄, …….. B₇

6. Let us join B₃C and from B₇ construct a line B₇C”|| B₃C which intersects the extended line segment BC at C’.

7. Construct C’A’||CA which intersects the extended line segment BA at A’.

So ∆A’B’C’ is the required triangle whose sides are 7/3 of the corresponding sides of ∆ABC.

It is given that

Segment B₆C’||B₃C

As the construction is not possible that segment B₆C’||B₃C as the similar triangle A’B’C’ has its sides 7/3 of the corresponding sides of triangle ABC.

Here B₇C’||B₃C.

Therefore, the statement is false.

✦ Try This: Construct any ∆ABC. Construct ∆ A’BC’ such that AB : A’B = 5:3 and ∆ ABC ~ ∆ A’BC’.

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

NCERT Exemplar Class 10 Maths Exercise 10.2 Problem 2

To construct a triangle similar to a given ∆ABC with its sides 7/3 of the corresponding sides of ∆ABC, draw a ray BX making acute angle with BC and X lies on the opposite side of A with respect to BC. The points B₁ , B₂ , ...., B₇ are located at equal distances on BX, B₃ is joined to C and then a line segment B₆C' is drawn parallel to B₃C where C' lies on BC produced. Finally, line segment A'C' is drawn parallel to AC. Write ‘True’ or ‘False’ and justify your answer

Summary:

The statement “To construct a triangle similar to a given ∆ABC with its sides 7/3 of the corresponding sides of ∆ABC, draw a ray BX making acute angle with BC and X lies on the opposite side of A with respect to BC. The points B₁ , B₂ , ...., B₇ are located at equal distances on BX, B₃ is joined to C and then a line segment B₆C' is drawn parallel to B₃C where C' lies on BC produced. Finally, line segment A'C' is drawn parallel to AC” is false

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