RS Aggarwal Class 6 Math Seventeenth Chapter Quadrilaterals Exercise 17A Solution
EXERCISE 17A
QUADRILATERALS – A simple closed figure bounded by four line segments is called a quadrilateral.
ADJACENT SIDES – Two sides of a quadrilateral which have a common end point are called its adjacent sides.
OPPOSITE SIDES – Two sides of a quadrilateral are called its opposite sides if they do not have a common end point.
ADJACENT ANGLES – Two angles of a quadrilateral having a common side are called its adjacent angles.
OPPOSITE ANGLES – Two angles of a quadrilateral which are not adjacent angles are known as the opposite angles of the quadrilateral.
CONVEX QUADRILATERAL – A quadrilateral in which the measure of each angle is less than 180o is called a convex quadrilateral.
CONCAVE QUADRILATERAL – A quadrilateral in which the measure of one of the angles is more than 180o is called a concave quadrilateral.
INTERIOR QUADRILATERAL – The part of the plane lying inside the boundary is called the interior of the quadrilateral.
EXTERIOR QUADRILATERAL – The part of the plane lying outside the boundary is called the exterior of the quadrilateral.
QUADRILATERAL REGION – The interior of the quadrilateral ABCD together with its boundary is called the quadrilateral region ABCD.
TRAPEZIUM – A quadrilateral having one and only one pair of parallel sides is called a trapezium.
PARALLELOGRAM – A quadrilateral in which both pairs of opposite sides are parallel is called a parallelogram.
RHOMBUS – A parallelogram in which all the sides are equal is called a rhombus.
RECTANGLE – A parallelogram in which each angle is a right angle is called a rectangle.
SQUARE – A parallelogram in which all the sides are equal and each angle is a right angle is called square.
KITE – A quadrilateral which has two pairs of equal adjacent sides but unequal opposite sides, is called a kite.
(1) In the adjacent figure, a quadrilateral has been shown.
Name: (i) Its diagonals,
Ans: AC, BD
(ii) Two pairs of opposite angles,
Ans: (AB, DC) and (AD, BC)
(iii) Two pairs of opposite angles,
Ans: (∠A,∠C),(∠B,∠D)
(iv) Two pairs of adjacent sides,
Ans: (AB, BC), (AD, DC)
(v) Two pairs of adjacent angles,
Ans: (∠A,∠B),(∠B,∠C)
(3) Two sides of a parallelogram are in the ratio 4 : 3. If its perimeter is 56 cm, find the lengths of its sides.
Solution: Let the two sides be 4x and 3x.
In a parallelogram, opposite sides are equal and parallel.
Ans: The length is (4×4) = 16 cm and side is (3×4) = 12 cm.
4) Name each of the following parallelograms:
(i) The diagonals are equal and the adjacent sides are unequal.
Ans: Rectangle
(ii) The diagonals are equal and the adjacent sides are equal.
Ans: Square
(iii) The diagonals are unequal and the adjacent sides are equal.
Ans: Rhombus
(5) What is a trapezium? When do you call a trapezium an isosceles trapezium?
Draw an isosceles trapezium. Measure its sides and angles.
Ans: TRAPEZIUM – A quadrilateral having one and only one pair of parallel sides is called a trapezium.
A trapezium is said to be an isosceles trapezium if its nonparallel sides are equal.
(6) Which of the following statements are true and which are false?
(a) The diagonals of a parallelogram are equal. = False
(b) The diagonals of a rectangle are perpendicular to each other. = False
(c) The diagonals of a rhombus are equal. = False
(7) Give reasons for the following:
(a) A square can be thought of as a special rectangle.
Reason: A rectangle with sides equal becomes a square.
(b) A square can be thought of as a special rhombus.
Reason: A rhombus with each angle a right angle becomes a square.
(c) A rectangle can be thought of as a special parallelogram.
Reason: A parallelogram with each angle a right angle becomes a rectangle.
(d) A square is also a parallelogram.
Reason: The opposite sides of a square are parallel, so it is a parallelogram.
(8) A figure is said to be regular if its sides are equal in length and angles are equal are equal in measure. What do you mean by a regular quadrilateral?
Ans: A regular quadrilateral is a square.
For more exercise solutions, Click Below –
Leave a Reply