Class 8 - Mathematics
Understanding Quadrilaterals - Exercise 3.4
Top Block 1
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. Since, squares have all sides are equal.
(b) True. Since, in rhombus, opposite angles are equal and diagonals intersect at mid-point.
(c) True. Since, squares have the same property of rhombus but not a rectangle.
(d) False. Since, all squares have the same property of parallelogram.
(e) False. Since, all kites do not have equal sides.
(f) True. Since, all rhombuses have equal sides and diagonals bisect each other.
(g) True. Since, trapezium has only two parallel sides.
(h) True. Since, all squares have also two parallel lines.
Question:2. Identify all the quadrilaterals that have:
(a) four sides of equal lengths.
(b) four right angles.
Answer :
(a) Rhombus and square have sides of equal length.
(b) Square and rectangle have four right angles.
Question:3. Explain how a square is:
(a) a quadrilateral
(b) a parallelogram
(c) a rhombus
(d) a rectangle
Answer :
(i) A square is a quadrilateral, since it has four equal lengths of sides.
(ii) A square is a parallelogram, since it contains both pairs of opposite sides equal.
(iii) A square is already a rhombus. Since, it has four equal sides and diagonals bisect at to each other.
(iv) A square is a parallelogram, since having each adjacent angle a right angle and opposite sides are equal.
Mddle block 1
Question:4. Name the quadrilateral whose diagonals:
(i) bisect each other.
(ii) are perpendicular bisectors of each other.
(iii) are equal.
Answer :
(i) If diagonals of a quadrilateral bisect each other then it is a rhombus, parallelogram, rectangle or square.
(ii) If diagonals of a quadrilateral are perpendicular bisector of each other, then it is a rhombus or square.
(iii) If diagonals are equal, then it is a square or rectangle.
Question:5. Explain why a rectangle is a convex quadrilateral.
Answer :
A rectangle is a convex quadrilateral since its vertex are raised and both of its diagonals lie in its interior.