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.What 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.What 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.Arjun 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.Which 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.If 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, 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. Danny 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. Ananya 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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