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MATHEMATICS [2 Mark Question Answer]

Mid - point Theorem and Intercept Theorem · ICSE STD 9 (ICSE - English Medium). 10 questions.

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[2 Mark Question Answer]

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10 questions · timed · auto-graded

Question 12 Marks
In the adjoining figure, ABCD is a kite in which $AB = AD$ and $CB = CD$. If $E , F , G$ are respectively the mid-points of $AB , AD$ and CD , prove that:
(i) $\angle EFG =90$,
(ii) If $GH \| FE$, then H bisects CB .
Image
Answer
[Hint. The diagonals of a kite intersect at right angles.]
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Question 22 Marks
In the adjoining figure, ABCD is a parallelogram in which E is the mid-point of DC and F is a point on AC such that $CF =\frac{1}{4} AC$. If EF is produced to meet BC in G , prove that G is the mid-point of BC .
Image
Answer
[Hint. Join BD and remember that the diagonals of a $\| g m$ bisect each other.]
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Question 32 Marks
In the given figure, LMN is a right triangle in which $\angle M =90$, P and Q are mid-points of LM and LN respectively. If $LM =9 cm, MN =12 cm$ and $LN =15 cm$, find :
(i) the perimeter of trapezium MNQP,
(ii) the area of trapezium MNQP.
Image
Answer
(i) 30 cm
(ii) $40.5 cm^2$
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Question 42 Marks
In the given figure $A , B , C$ and D are midpoints of PQ, QR, RS and PS respectively. $E , F , G$ and H are mid-points of $AB , BC$, CD and AD respectively. Which type of quadrilaterals are ABCD and EFGH ?
Image
Answer
parallelogram
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Question 52 Marks
In the given figure, $\triangle A B C$ is a scalene triangle in which $\angle B =90 . P$ is the midpoint of $AB , PQ \| BC$ and $QM \perp BC$. Which type of quadrilateral is PQMB ?
Image
Answer
rectangle
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Question 62 Marks
Show that the quadrilateral formed by joining the mid-points of the pairs of adjacent sides of a square is a square.
Answer
self
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Question 72 Marks
Show that the quadrilateral formed by joining the mid-points of the pairs of adjacent sides of a rectangle is a rhombus.
Image
Answer
self
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Question 82 Marks
In the adjoining figure, ABCD is a kite in which $A B=A D$ and $C B=C D$. If $E, F, G$ are respectively the mid-points of $A B, A D$ and $C D$, prove that:
(i) $\angle EFG =90^{\circ}$,
(ii) If GH \| FE , then H bisects CB .
Image
Answer
self
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Question 92 Marks
In the adjoining figure, ABCD is a parallelogram in which $E$ is the mid-point of $D C$ and $F$ is a point on $A C$ such that $CF =\frac{1}{4} AC$. If EF is produced to meet BC in G , prove that G is the mid-point of BC .
Image
Answer
self
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Question 102 Marks
In the given figure, LMN is a right triangle in which $\angle M =90^{\circ}$, P and Q are mid-points of LM and LN respectively. If $LM =9 cm, MN =12 cm$ and $LN =15 cm$, find :
(i) the perimeter of trapezium MNQP,
(ii) the area of trapezium MNQP.
Image
Answer
(i) 30 cm
(ii) $40.5 cm^2$
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[2 Mark Question Answer] - MATHEMATICS STD 9 Questions - Vidyadip