Class 9 The Mid-point Theorem — practice questions with answers
Geometry — Quadrilaterals · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
1. In a triangle, the segment joining the mid-points of two sides is parallel to the third side and equal to:
Athe third side
Bhalf the third side
Ctwice the third side
Done-third of the third side
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Answer: B) half the third side
The Mid-point Theorem states the segment joining mid-points of two sides is parallel to the third side and equal to half of it.
2. The medial triangle divides the original triangle into how many triangles of equal area?
A2
B3
C4
D6
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Answer: C) 4
The three midsegments split the triangle into 4 congruent (equal-area) smaller triangles.
3. If midsegment DE = (x + 2) cm and the parallel side BC = (3x - 2) cm, find x.
A5
B7
C6
D12
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Answer: C) 6
BC = 2 DE: 3x - 2 = 2(x + 2) = 2x + 4, so x = 6.
4. In triangle ABC, M is the mid-point of AB and a line MN parallel to BC meets AC at N. It is given AN = 5 cm. Farhan claims AC = 10 cm. Find AC and check his claim.
AAC = 10 cm, claim correct
BAC = 5 cm, claim wrong
CAC = 15 cm, claim wrong
DAC = 2.5 cm, claim wrong
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Answer: A) AC = 10 cm, claim correct
By the converse, N is the mid-point of AC, so AC = 2 x AN = 2 x 5 = 10 cm. Farhan is correct.
5. In quadrilateral ABCD, the mid-points P, Q, R, S of the sides are joined in order to form a parallelogram PQRS. It is observed that PQRS turns out to be a rectangle. What special property must the diagonals AC and BD of ABCD have?
Athey are perpendicular
Bthey are equal
Cthey bisect each other
Dthey are parallel
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Answer: A) they are perpendicular
Sides of PQRS are parallel to the diagonals AC and BD. For PQRS to have right angles (a rectangle), the diagonals AC and BD must be perpendicular.