# NCERT Class 8 Mathematics Solutions: Chapter 3 –Understanding Quadrilaterals Exercise 3.4 Part 1

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**Question: 1 **State whether true or false:

(a) All rectangles are squares.

(b) All rhombuses are parallelograms.

(c) All squares are rhombuses and also rectangles.

(d) All squares are not parallelograms.

(e) All kites are rhombuses.

(f) All rhombuses are kites.

(g) All parallelograms are trapeziums.

(h) All squares are trapeziums.

**Answer:**

(a) False: - All square are rectangle but All rectangles cannot squares, In square all side are equal.

(b) True: - In rhombus opposite sides of a rhombus are equal and parallel to each other.

(c)True:- Squares have the same property of rhombus but not a rectangle. All squares are also rectangles as each internal angle measures 90°.

(d) False: - All squares have the same property of parallelogram.

(e) False: - All squares are parallelograms as opposite sides are equal and parallel; all kites do not have equal sides.

(f) True: All rhombuses have equal sides and diagonals bisect each other, A rhombus also has two distinct consecutive pairs of sides of equal length.

(g) False: - All parallelograms are not trapezium since opposite of parallelogram are equal and parallel.

(h) True: - All squares have a pair of parallel sides

**Question: 2 **Identify all the quadrilaterals that have:

(a) Four sides of equal lengths.

(b) Four right angles.

**Answer:**

(a)

** - **Rhombus and square have 4 equal side lengths.

(b)

- Square and rectangle are the quadrilaterals, it has four right angles.

**Question: 3 **Explain how a square is:

(i) a quadrilateral

(ii) a parallelogram

(iii) a rhombus

(iv) a rectangle

**Answer:**

(i)** A Quadrilateral: - **A square is a quadrilateral. If having four sides.

(ii)** A Parallelogram**:-A square is a parallelogram. If it contains both pairs of opposite sides equal.

(iii)** A rhombus: - **A square is already a rhombus. If it has four equal sides and diagonals bisect at 90 to each other.

(iv) **A rectangle: - **A square is a rectangle. If opposite side are equal and angles are right angles.