NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.4
Ex 3.4 Class 8 Maths 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.
Solution:
(a)
False
(b) True
(c) True
(d) False
(e) False
(f) True
(g) True
(h) True
Ex 3.4 Class 8 Maths Question 2.
Identify all the quadrilaterals that have(a) four sides of equal length
(b) four right angles
Solution:
(a) Squares and rhombuses have four sides of
equal length.
(b) Rectangles and squares have four right angles.
Ex 3.4 Class 8 Maths Question 3.
Explain how a square is(i) a quadrilateral
(ii) a parallelogram
(iii) a rhombus
(iv) a rectangle
Solution:
(i) A square is a quadrilateral because it is a
four-sided polygon.
(ii) A square is a parallelogram due to the following properties:
(a) Opposite sides are equal and parallel.
(b) Opposite angles are equal.
(iii) A square is a rhombus because its all sides are equal and opposite sides
are parallel.
(iv) A square is a rectangle because its opposite sides are equal and parallel
and has equal diagonals.
Ex 3.4 Class 8 Maths Question 4.
Name the quadrilaterals whose diagonals(i) bisect each other
(ii) are perpendicular bisectors of each other
(iii) are equal
Solution:
(i)
Parallelogram, rectangle, square and rhombus
(ii) Square and rhombus
(iii) Square and rectangle
Ex 3.4 Class 8 Maths Question 5.
Explain why a rectangle is a convex quadrilateral.Solution:
In a rectangle, both of its diagonals lie in its
interior and each of its angle measures less than 180°. Hence, a rectangle is a
convex quadrilateral.
Ex 3.4 Class 8 Maths Question 6.
ABC is a right-angled triangle and O is the midpoint 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).
Solution:
Since the right-angled triangle ABC makes a
rectangle ABCD by the dotted lines.
Therefore, OA = OB = OC = OD [Diagonals of a rectangle are equal and bisect
each other]
Hence, O is equidistant from A, B and C.
Related Links:
NCERT Solutions for Maths Class 9
NCERT Solutions for Maths Class 10
NCERT Solutions for Maths Class 11