# 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:**

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