Given a rhombus ABCD in which AB = 4 cm and ∠ABC = 60°, divide it into two triangles say, ABC and ADC. Construct the triangle AB'C' similar to ∆ABC with scale factor 2/3. Draw a line segment C'D' parallel to CD where D' lies on AD. Is AB'C'D' a rhombus? Give reasons

Solution:

Steps of Construction

1. Draw a rhombus ABCD with AB = 4 cm and ∠ABC = 60°

2. Now join AC. ABCD is divided into two triangles ABC and ADC

3. Draw a triangle AB’C’ similar to ABC with a scale factor 2/3

4. Construct a line segment C’D’ which is parallel to CD

We know that

AB’/AB = 2/3 = AC’/AC

Here

AC’/AC = C’D’/CD

So we get

= AD’/AD = 2/3

AB’ = B’C’ = C’D’ = AD’ = 2/3 AB

Therefore, AB’C’D’ is a rhombus.

✦ Try This: Given a rhombus ABCD in which AB = 5 cm and ∠ABC = 30°, divide it into two triangles say, ABC and ADC. Construct the triangle AB'C' similar to ∆ABC with scale factor 3/4. Draw a line segment C'D' parallel to CD where D' lies on AD. Is AB'C'D' a rhombus? Give reasons.

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

NCERT Exemplar Class 10 Maths Exercise 10.4 Sample Problem 1

Given a rhombus ABCD in which AB = 4 cm and ∠ABC = 60°, divide it into two triangles say, ABC and ADC. Construct the triangle AB'C' similar to ∆ABC with scale factor 2/3. Draw a line segment C'D' parallel to CD where D' lies on AD. Is AB'C'D' a rhombus? Give reasons

Summary:

Given a rhombus ABCD in which AB = 4 cm and ∠ABC = 60°, it is divided into two triangles say, ABC and ADC. A triangle AB'C' similar to ∆ABC with scale factor 2/3 is constructed. A line segment C'D' parallel to CD where D' lies on AD is drawn. Yes, AB'C'D' a rhombus

☛ Related Questions:

• Two line segments AB and AC include an angle of 60° where AB = 5 cm and AC = 7 cm. Locate points P a . . . .
• Draw a parallelogram ABCD in which BC = 5 cm, AB = 3 cm and ∠ABC = 60°, divide it into triangles BCD . . . .
• Draw two concentric circles of radii 3 cm and 5 cm. Taking a point on outer circle construct the pai . . . .