# The figure obtained by joining the mid-points of the sides of a rhombus, taken in order, is

a. a rhombus

b. a rectangle

c. a square

d. any parallelogram

**Solution:**

Consider ABCD as a rhombus with P, Q, R and S as the midpoints of AB, BC, CD and DA.

From the property of a rhombus, AC || PQ

In Δ ACB and ΔPQB

∠BAC = ∠BPQ and ∠BCA = ∠BQP

∠ABC = ∠PBQ are same angles

Here Δ ABC is congruent to Δ PBQ

AC/PQ = BC/BQ

PQ = 1/2 AC

Consider Δ BCD and Δ RCQ

RQ = 1/2 BD

Similarly Δ ADC and Δ SDR

SR = 1/2 AC

SP = 1/2 BD

As the opposite sides are equal PQ = SR and RQ = SP

We know that

∠APS + ∠SPQ + ∠BPQ = 180°

∠ABD + ∠SPQ + ∠BAC = 180°

1/2 ∠ABC + ∠SPQ + 1/2 ∠BAD = 180°

∠SPQ + 1/2 (∠ABC + ∠BAD) = 180°

Using the property of rhombus

∠SPQ + 1/2 (180°) = 180°

∠SPQ = 90°

∠PQR = ∠QRS = RSP = 90°

Opposite sides are equal and all angles are 90°

So it is a rectangle.

Therefore, the figure obtained is a rectangle.

**✦ Try This: **The figure obtained by joining the mid-points of the adjacent sides 8 cm and 6 cm a. a rhombus, b. a rectangle, c. a square, d. any parallelogram

**☛ Also Check:** NCERT Solutions for Class 9 Maths Chapter 8

**NCERT Exemplar Class 9 Maths Exercise 8.1 Problem 9**

## The figure obtained by joining the mid-points of the sides of a rhombus, taken in order, is , a. a rhombus, b. a rectangle, c. a square, d. any parallelogram

**Summary:**

The figure obtained by joining the mid-points of the sides of a rhombus, taken in order, is a rectangle

**☛ Related Questions:**

- D and E are the mid-points of the sides AB and AC of ∆ABC and O is any point on side BC. O is joined . . . .
- The figure formed by joining the mid-points of the sides of a quadrilateral ABCD, taken in order, is . . . .
- The diagonals AC and BD of a parallelogram ABCD intersect each other at the point O. If ∠DAC = 32º a . . . .

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