Competency Based Questions Chapter 8 Quadrilaterals

Hint: Apply angle sum property of quadrilateral in order to find the value of the unknown angle.

Question.1. A quadrilateral PKMN is shown below.cbe-questions-maths-class-9-ch-8-q-1What is the measure of \angleNPK?

(a) 124°
(b) 104°
(c) 84°
(d) 64°

Question.2. In quadrilateral BDGH, if \angleBDG = 2\angleDGH and \angleBHG = 3\angleHBD, which of the following is true about \angleBDG?

(a) \angleDGH = \frac{1}{3}(360° – 3\angleHBD)
(b) \angleDGH = \frac{1}{2}(360° – 4\angleHBD)
(c) \angleDGH = \frac{1}{3}(360° – 4\angleHBD)
(d) \angleDGH = \frac{1}{2}(360° – 3\angleHBD)

Ans.1. (a) 124°
Ans.2. (a) \angleDGH = \frac{1}{3}(360° – 3\angleHBD)

Hint: List the properties of quadrilaterals in order to classify real life objects into different types of Quadrilaterals.

Question.3. Ravi cut two pieces of marble as shown.cbe-questions-maths-class-9-ch-8-q-3What is common about the shapes of both the pieces?

(a) Both are squares.
(b) Both are rhombus.
(c) Both are rectangles.
(d) Both are parallelograms.

Question.4. A clock and a scale are shown below.cbe-questions-maths-class-9-ch-8-q-4Arjun claims that the clock shown is a square but not a rhombus and Vinod claims that the ruler shown is a rectangle but not a parallelogram.
Whose claim is/are correct?

(a) Only Arjun
(b) Only Vinod
(c) Both of them
(d) None of them

Ans.3. (d) Both are parallelograms.
Ans.4. (d) None of them

Hint: List the properties of parallelogram in order to identify if a given quadrilateral is a parallelogram.

Question.5. Which of the following is NOT a property of a quadrilateral that is a parallelogram?

(a) Diagonals of a quadrilateral bisect each other
(b) A pair of adjacent sides of a quadrilateral is equal
(c) Each pair of opposite sides of a quadrilateral is equal
(d) Each pair of opposite angles of a quadrilateral is equal

Question.6. Some quadrilaterals are shown below.cbe-questions-maths-class-9-ch-8-q-6Which of the following quadrilaterals are parallelograms?

(a) Only i and v
(b) Only i, ii and v
(c) Only ii, iii and iv
(d) Only ii, iv and v

Ans.5. (b) A pair of adjacent sides of a quadrilateral is equal
Ans.6. (a) Only i and v

Hint: Apply properties of parallelogram in order to find

(a) an unknown angle
(b) an unknown side

Question.7. A parallelogram ABCD is shown below.cbe-questions-maths-class-9-ch-8-q-7If the perimeter of the parallelogram is 36 cm, what is the length of AB?

(a) 5 cm
(b) 8 cm
(c) 10 cm
(d) 12 cm

Question.8. In the parallelogram shown below,cbe-questions-maths-class-9-ch-8-q-8 PR = 16 cm, PQ = 10 cm.
What is the length of the diagonal SQ?

(a) 6 cm
(b) 8 cm
(c) 12 cm
(d) 16 cm

Ans.7. (c) 10 cm
Ans.8. (c) 12 cm

Hint: Prove the midpoint theorem of triangles using concepts of congruency and transversal angles in order to extend the application to quadrilaterals.

Question.9. A figure is shown below where B and D are midpoints of sides MK and MA. cbe-questions-maths-class-9-ch-8-q-9Danny constructs a ray KR such that MAǁKR to prove the midpoint theorem.
He proves ∆MBD is congruent to ∆KBR by ASA congruency. Which of the following is the next step in the proof of the midpoint theorem?

(a) show that BD = RB
(b) show that BD = BK
(c) show that MB = RK
(d) show that MD = BK

Question.10. In the figure shown, Points N and O are midpoints of sides KL and KM of ∆KLM. cbe-questions-maths-class-9-ch-8-q-10Ananya wants to prove NOǁLM. She constructs a ray MP such that KLǁMP.
She first proves ∆KON ≅ ∆MOP. Which of the following justifies her step of proof?

(a) ∆KON ≅ ∆MOP by SAS congruency because KO = OM, NO = OP and \angleKON = \angleMOP.
(b) ∆KON ≅ ∆MOP by SAS congruency because KO = OM, KN = MP and \angleNKO = \anglePMO.
(c) ∆KON ≅ ∆MOP by ASA congruency because NO = OP, \angleKON = \angleMOP and \angleNKO = \anglePMO.
(d) ∆KON ≅ ∆MOP by ASA congruency because KO = OM, \angleKON = \angleMOP and \angleNKO = \anglePMO.

Ans.9. (a) show that BD = RB
Ans.10. (d) ∆KON ≅ ∆MOP by ASA congruency because KO = OM, \angleKON = \angleMOP and \angleNKO = \anglePMO.

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