Practice Set 5.3 Geometry 9th Std Maths Part 2 Answers Chapter 5 Quadrilaterals
Solution & Step-by-Step Answer:
i. AC = 8 cm …(i) [Given] □ABCD is a rectangle [Given] ∴ BD = AC [Diagonals of a rectangle are congruent] ∴ BD = 8 cm [From (i)] BO = BD [Diagonals of a rectangle bisect each other] ∴ BO = x 8 ∴ BO = 4 cm
ii. side AD || side BC and seg AC is their transversal. [Opposite sides of a rectangle are parallel]
∴ ∠ACB = ∠CAD [Alternate angles]
∠ACB = 35° [ ∵∠CAD = 35°]
∴ BO = 4 cm, ∠ACB = 35°
Solution & Step-by-Step Answer:
i. PQ = 7.5 cm [Given] □PQRS is a rhombus. [Given] ∴ QR = PQ [Sides of a rhombus are congruent] ∴ QR = 7.5 cm
ii. ∠QPS = 75° [Given]
∠QPS + ∠PQR = 180° [Adjacent angles of a rhombus are supplementary]
∴ 75° + ∠PQR = 180°
∴ ∠PQR = 180° – 75°
∴ ∠PQR =105°
iii. ∠SRQ = ∠QPS [Opposite angles of a rhombus]
∴ ∠SRQ = 75°
∴ QR = 7.5 cm, ∠PQR = 105°,
∠SRQ = 75°
Solution & Step-by-Step Answer:
□IJKL is a square. [Given] ∴ seg IK ⊥ seg JL [Diagonals of a square are perpendicular to each other] ∠ IMJ=90° ∠ JIL 90° ……. (i) [Angle of a square]
ii. ∠JIK = ∠JIL [Diagonals of a square bisect the opposite angles]
∠JIK = (90°) [From (i)
∴ ∠JIK = 45°
∠IJK = 90° (ii) [Angle of a square]
iii. ∠LJK = ∠IJK [Diagonals of a square bisect the opposite angles]
∠LJK = (90°) [From (ii)]
∴ ∠LJK = 45°
∴ ∠LJK = 90°, ∠JIK = 45°, ∠LJK=45°
Solution & Step-by-Step Answer:
i. Let □ABCD be the rhombus. AC = 20 cm, BD = 21 cm
ii. In ∆AOB, ∠AOB = 90° [Diagonals of a rhombus are prependicular to each other]
∴ AB2= AO2+ BO2[Pythagoras theorem]
iii. Perimeter of □ABCD
= 4 x AB = 4 x 14.5 = 58 cm
∴ The side and perimeter of the rhombus are 14.5 cm and 58 cm respectively.
Solution & Step-by-Step Answer:
i. False. All the sides of a rhombus are congruent, while the opposite sides of a parallelogram are congruent. ii. False. All the angles of a rectangle are congruent, while the opposite angles of a rhombus are congruent. iii. True. The opposite sides of a parallelogram are parallel and congruent. Also, its opposite angles are congruent. The opposite sides of a rectangle are parallel and congruent. Also, all its angles are congruent. iv. True. The opposite sides of a rectangle are parallel and congruent. Also, all its angles are congruent. All the sides of a square are parallel and congruent. Also, all its angles are congruent. v. True. All the sides of a rhombus are congruent. Also, its diagonals are perpendicular bisectors of each other. All the sides of a square are congruent. Also, its diagonals are perpendicular bisectors of each other. vi. False. All the angles of a rectangle are congruent, while the opposite angles of a parallelogram are congruent.