# Understanding Quadrilaterals : Exercise 3.4 (Mathematics NCERT Class 8th)

Q.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.
Sol. (a) False
(b) True
(c) True
(d) False
(e) False
(f) True
(g) True
(h) True

Q.2 Identify all the quadrilaterals that have.
(a) four sides of equal length
(b) four right angles
Sol. (a) Rhombus and Square have four sides of equal length.
(b) Square and rectangle have four right angles.

Q.3 Explain how a square is.
(ii) a parallelogram
(iii) a rhombus
(iv) a rectangle
Sol. (i) A square is a quadrilateral since it has four sides.
(ii) A square is a parallelogram since its opposite sides are parallel to each other.
(iii) A square is a rhombus since it has four equal sides and diagonals bisect at 90ᵒ to each other.
(iv) A square is a rectangle since its each interior angle measures 90ᵒ.

Q.4 Name the quadrilaterals whose diagonals.
(i) bisect each other (ii) are perpendicular bisectors of each other (iii) are equal
Sol. (i) Rhombus, parallelogram, rectangle and square are quadrilaterals whose diagonals bisect each other.
(ii) Rhombus and square are quadrilaterals whose diagonals are perpendicular bisectors of each other.
(iii) Square and rectangle are quadrilaterals whose diagonals are equal.

Q.5 Explain why a rectangle is a convex quadrilateral.
Sol. A rectangle has two diagonals and both lies in the interior part of the rectangle. Hence, a rectangle is a convex quadrilateral.

Q.6 ABC is a right-angled triangle and O is the mid point of the side opposite to the right angle. Explain why O is equidistant from A, B and C. (The dotted lines are drawn additionally to help you). Sol. For the given right-angled triangle ABC, draw lines AD and DC such that || and || . Also, AD = BC and AB = DC.
Hence, now ABCD is a rectangle as opposite sides are equal and parallel to each other and all the interior angles are of 90ᵒ.
We know that, in rectangle diagonals are of equal length and they bisect each other.
Therefore, AO = OC = BO = OD.
Thus, O is equidistant from A, B and C.

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