Haryana State Board HBSE 8th Class Maths Solutions Chapter 3 Understanding Quadrilaterals Ex 3.4 Textbook Exercise Questions and Answers.
Haryana Board 8th Class Maths Solutions Chapter 3 Understanding Quadrilaterals Exercise 3.4
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 paralellograms.
(e) All kites are rhombuses.
(f) All rhombuses are kites.
(g) All parallelograms are trapeziums.
(h) All squares are trapeziums.
Answer:
(a) False,
(b) True,
(c) True,
(d) False,
(e) False,
(f) True,
(g) True,
(h) True.
Question 2.
Identify all the quadrilaterals that have
(a) Four sides of equal length.
(b) Four right angles.
Answer:
(a) Rhombus; square,
(b) Square, rectangle.
Question 3.
Explain how a square is
(i) a quadrilateral
(ii) a parallelogram
(iii) a rhombus
(iv) a rectangle.
Answer:
(i) A square has four sides; so it is a quadrilateral.
(ii) A square has its opposite sides parallel; so it is a parallelogram.
(iii) A square is a parallelogram with all 4 sides equal; so it is a rhombus.
(iv) A square is a parallelogram with each angle a right angle; so it is a rectangle.
Question 4.
Name the quadrilaterals whose diagonals
(i) bisect each other.
(ii) are perpendicular bisectors of each other.
(iii) are equal.
Answer:
(i) The diagonals of a parallelogram, a rhombus, a square and a rectangle bisect each other.
(ii) Rhombus; square.
(iii) Square; rectangle.
Question 5.
Explain why a rectangle is a convex quadrilateral.
Answer:
Both of its diagonals lie in its interior.
Question 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).
Answer:
\(\overline{\mathrm{AD}}\) || \(\overline{\mathrm{BC}}\) and \(\overline{\mathrm{AB}}\) || \(\overline{\mathrm{CD}}\). So ABCD is a ||gm. The mid-point of diagonal \(\overline{\mathrm{AC}}\) is O. So, O is equidistant from A, B and C.
Hence, OA = OB = OC.