Class 8 math exercise 3.3

NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.3 • • • • • NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Exercise 3.3 Ex 3.3 Class 8 Maths Question 1. Given a parallelogram ABCD. Complete each statement along with the definition or property used. (i) AD = ………… (ii) ∠DCB = ……… (iii) OC = ……… (iv) m∠DAB + m∠CDA = …….. Solution: (i) AD = BC [Opposite sides of a parallelogram are equal] (ii) ∠DCB = ∠DAB [Opposite angles of a parallelogram are equal] (iii) OC = OA [Diagonals of a parallelogram bisect each other] (iv) m∠DAB + m∠CDA = 180° [Adjacent angles of a parallelogram are supplementary] Ex 3.3 Class 8 Maths Question 2. Consider the following parallelograms. Find the values of the unknowns x, y, z. Solution: (i) ABCD is a parallelogram. ∠B = ∠D [Opposite angles of a parallelogram are equal] ∠D = 100° ⇒ y = 100° ∠A + ∠B = 180° [Adjacent angles of a parallelogram are supplementary] ⇒ z + 100° = 180° ⇒ z = 180° – 100° = 80° ∠A = ∠C [Opposite angles of a ||gm] x = 80° Hence x = 80°, y = 100° and z = 80° (ii) PQRS is a parallelogram. ∠P + ∠S = 180° [Adjacent angles of parallelogram] ⇒ x + 50° = 180° x = 180° – 50° = 130° Now, ∠P = ∠R [Opposite angles are equal] ⇒ x = y ⇒ y = 130° Also, y = z [Alternate angles] z = 130° Hence, x = 130°, y = 130° and z = 130° (iii) ABCD is a rhombus. [∵ Diagonals intersect at 90°] x = 90° Now in ∆OCB, x + y + 30° = 180° (Angle sum property) ⇒ 90° + y + 30° = 180° ⇒ y + 120° = 180° ⇒ y = 180...

• • • Board CBSE Textbook NCERT Class Class 8 Subject Maths Chapter Chapter 3 Chapter Name Understanding Quadrilaterals Exercise Ex 3.3 Number of Questions Solved 12 Category NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.3 Question 1. Given a parallelogram ABCD. Complete each statement along with the definition with the definition or property used. (i) AD = ……… (ii) ∠DCB = ……………. (iii) OC = ………………. (iv) m∠DAB + m∠CDA = ………….. Solution. (i) AD = BC Opposite sides of a parallelogram are equal (ii) ∠DCB = ∠DAB Opposite angles of a parallelogram are equal (iii) OC = OA ∵ Diagonals of a parallelogram bisect each other (iv) m∠DAB + m∠CDA = 180° ∵ Adjacent angles of a parallelogram are supplementary. Question 2. Consider the following parallelo¬grams. Find the values of the unknowns x, y, z. Solution. (i) y = 100° Opposite angles of a parallelogram are equal x + 100° = 180° Adjacent angles in a parallelogram are supplementary ⇒ x = 180° – 100° ⇒ x = 80° ⇒ z – x = 80° Opposite angles of a parallelogram are of equal measure (ii) x + 50° = 180° Adjacent angles in a parallelogram are supplementary ⇒ x = 180° – 50° = 130° ⇒ y = x = 130° The opposite angles of a parallelogram are of equal measure 180° – z = 50° Opposite angles of a parallelogram are of equal measure ⇒ z = 180° – 50° = 130° (iii) x = 90° Vertically opposite angles are equal x + y + 30° = 180° By angle sum property of a triangle ⇒ 90° + y + 30° = 180° ⇒ 120° + y = 180° ⇒ y = 180° – 120° = ...