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Maths 2 Mark Question

Quadrilaterals · Maharashtra Board STD 9 (MSBSHSE - English Medium). 10 questions.

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2 Mark Question

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10 questions · self-marked practice — reveal the answer and mark yourself.

Question 12 Marks
To verify the different properties of quadrilaterals.

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Answer
Material: A piece of plywood measuring about 15 cm x 10 cm, 15 thin screws, twine, scissor.
Note: On the plywood sheet, fix five screws in a horizontal row keeping a distance of 2 cm between any two adjacent screws. Similarly make two more rows of screws exactly below the first one. Take care that the vertical distance between any two adjacent screws is also 2 cm.
With the help of the screws, make different types of quadrilaterals of twine. Verify the properties of sides and angles of the quadrilaterals.
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Question 22 Marks
Draw a parallelogram PQRS. Draw diagonals PR and QS. Denote the intersection of diagonals by letter O. Compare the two parts of each diagonal with a divider. What do you find?

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Answer
seg OP = seg OR, and seg OQ = seg OS
Thus we can conclude that, point O divides the diagonals PR and QS in two equal parts.
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Question 42 Marks
Prove the Theorem : A quadrilateral is a parallelogram if a pair of its opposite sides is parallel and congruent.
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Question 52 Marks
$\mathrm{ABCD}$ is a parallelogram. If $\angle \mathrm{A}=(4 x+13)^{\circ}$ and $\angle \mathrm{D}=(5 x-22)^{\circ}$ then find the measures of $\angle \mathrm{B}$ and $\angle \mathrm{C}$.
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Question 62 Marks
$\square \mathrm{PQRS}$ is a parallelogram. $\mathrm{PQ}=3.5, \mathrm{PS}=5.3 \angle \mathrm{Q}=50^{\circ}$ then find the lengths of remaining sides and measures of remaining angles.
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Question 92 Marks
Points D and E are the midpoints of side AB and side AC of ∆ABC respectively. Point F is on ray ED such that ED = DF. Prove that □AFBE is a parallelogram. For this example write ‘given’ and ‘to prove’ and complete the proof.

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Given: D and E are the midpoints of side AB and side AC respectively.
ED = DF
To prove: □AFBE is a parallelogram.

Answer
Proof:
seg AB and seg EF are the diagonals of □AFBE.
seg AD ≅ seg DB [Given]
seg DE ≅ seg DF [Given]
∴ Diagonals of □AFBE bisect each other.
∴ □AFBE is a parallelogram. [ By test of parallelogram]
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Question 102 Marks
Using opposite angles test for parallelogram, prove that every rectangle is a parallelogram.

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Given:
□ABCD is a rectangle.
To prove: Rectangle ABCD is a parallelogram.

Answer
Proof:
□ABCD is a rectangle.
∴ ∠A ≅ ∠C = 90° [Given]
∠B ≅ ∠D = 90° [Angles of a rectangle]
∴ Rectangle ABCD is a parallelogram. [A quadrilateral is a parallelogram, if pairs of its opposite angles are congruent]
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