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A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.

Draw a triangle ABC in which AB = 4 cm, BC = 6 cm and AC = 9 cm. Construct a triangle similar to ∆ABC with scale factor 3/2. Justify the construction. Are the two triangles congruent? Note that all the three angles and two sides of the two triangles are equal

Solution:

Steps of Construction:

1. Construct a line segment BC = 6 cm

2. Taking B as centre and 4 cm radius, construct an arc

3. Taking C as centre and 9 cm radius, construct another arc intersecting the previous arc at A

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

5. Through the point B, construct an acute angle ∠CBX on the side opposite to the vertex A

6. Mark three arcs B1, B2 and B3 on BX where BB1 = B1B2 = B2B3

7. Join B2C

8. Construct B3C’||B2C which intersects the extended line segment BC at the point C’

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

∆A’BC’ is the required triangle

Draw a triangle ABC in which AB = 4 cm, BC = 6 cm and AC = 9 cm. Construct a triangle similar to ∆ABC with scale factor 3/2. Justify the construction. Are the two triangles congruent? Note that all the three angles and two sides of the two triangles are equal

Justification:

We know that

B3C’ || B2C

BC/CC’ = 2/1

Here

BC’/BC = (BC + CC’)/BC = 1 + CC’/BC

= 1 + 1/2

= 3/2

Similarly

CC’||CA

∆ABC is similar to ∆A’BC’

A’B/AB = BC’/BC = CC’/AC = 3/2

Therefore, the two triangles are not congruent.

✦ Try This: Draw a triangle ABC in which AB = 2 cm, BC = 3 cm and AC = 10 cm. Construct a triangle similar to ∆ABC with scale factor 2/3. Justify the construction. Are the two triangles congruent? Note that all the three angles and two sides of the two triangles are equal.

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

NCERT Exemplar Class 10 Maths Exercise 10.4 Problem 7

Draw a triangle ABC in which AB = 4 cm, BC = 6 cm and AC = 9 cm. Construct a triangle similar to ∆ABC with scale factor 3/2. Justify the construction. Are the two triangles congruent? Note that all the three angles and two sides of the two triangles are equal

Summary:

A triangle ABC with AB = 4 cm, BC = 6 cm and AC = 9 cm is drawn. A triangle similar to ∆ABC with scale factor 3/2 is constructed. No, the two triangles are not congruent

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