Keeping the examination point of view in mind the mathematicsandinformationtechnology.com team has prepared NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals exercise 3.4. The NCERT Solutions for chapter Understanding Quadrilaterals solutions explains the easy and simple way to solve the problems. By understanding these ways in NCERT Solutions for Class 8, students will be confident while solving such problems found in Chapter 3 Understanding Quadrilaterals.
State whether True or False.
(a) All rectangles are squares- False. All squares are rectangles but all rectangles are not squares.
(b) All rhombuses are parallelograms-True. Opposite sides of a rhombus are equal and parallel to each other..
(c) All squares are rhombuses and also rectangles-True. All squares are rhombuses as all sides of a square are of equal lengths. All squares are also rectangles as each internal angle measures 90°.
(d) All squares are not parallelograms-False. All squares are parallelograms as opposite sides are equal and parallel.
(e) All kites are rhombuses-False. A kite does not have all sides of the same length.
(f) All rhombuses are kites.- True. A rhombus also has two distinct consecutive pairs of sides of equal length.
(g) All parallelograms are trapeziums.-True. All parallelograms have a pair of parallel sides.
(h) All squares are trapeziums-True. All squares have a pair of parallel sides.
Question 2:
Identify all the quadrilaterals that have
(a) four sides of equal length
(b) four right angles
Answer:
(a) Rhombus and Square are the quadrilaterals that have 4 sides of equal length.
(b) Square and rectangle are the quadrilaterals that have 4 right angles.
Question 3:
Explain how a square is.
(i) a quadrilateral
(ii) a parallelogram
(iii) a rhombus
(iv) a rectangle
Answer:
(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 its four sides are of the same length.
(iv) A square is a rectangle since each interior angle measures 90°.
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, rhombus, square, and rectangle bisect each other.
(ii) The diagonals of a rhombus and square act as perpendicular bisectors.
(iii) The diagonals of a rectangle and square are equal.
Question 5:
Explain why a rectangle is a convex quadrilateral.
Answer:
In a rectangle, there are two diagonals, both lying in the interior of the rectangle.
Hence, it is a convex quadrilateral.
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).
Identify all the quadrilaterals that have
(a) four sides of equal length
(b) four right angles
Answer:
(a) Rhombus and Square are the quadrilaterals that have 4 sides of equal length.
(b) Square and rectangle are the quadrilaterals that have 4 right angles.
Question 3:
Explain how a square is.
(i) a quadrilateral
(ii) a parallelogram
(iii) a rhombus
(iv) a rectangle
Answer:
(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 its four sides are of the same length.
(iv) A square is a rectangle since each interior angle measures 90°.
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, rhombus, square, and rectangle bisect each other.
(ii) The diagonals of a rhombus and square act as perpendicular bisectors.
(iii) The diagonals of a rectangle and square are equal.
Question 5:
Explain why a rectangle is a convex quadrilateral.
Answer:
In a rectangle, there are two diagonals, both lying in the interior of the rectangle.
Hence, it is a convex quadrilateral.
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:
Draw lines AD and DC such that AD||BC, AB||DC
AD = BC, AB = DC
ABCD is a rectangle as opposite sides are equal and parallel to each other and all the interior angles are of 90º.
In a rectangle, diagonals are of equal length and also these bisect each other.
Hence, AO = OC = BO = OD
Thus, O is equidistant from A, B, and C.
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