Same chapter1 markDifficulty: Medium
D and E are the mid-points of AB and AC of triangle ABC. If DE = 5 cm, then BC is:
Mid-point Theorem
4 marksDifficulty: Hard
Prove that the quadrilateral formed by joining the mid-points of the sides of any quadrilateral is a parallelogram.
Original Khojo Papers practice question — not from a past board paper.
Answer
Joining a diagonal of the quadrilateral splits it into two triangles. In each triangle the segment joining the mid-points of two sides is parallel to that diagonal and half its length. The two segments are therefore equal and parallel to each other, and so are the other pair, so the figure is a parallelogram.
No citable source has been recorded for this record. Treat it as practice material, not as fact.
Explanation
The result holds whatever the shape of the original quadrilateral.
Related questions
From the same topic and chapter, at a similar level.
Same chapter3 marksDifficulty: Medium
In a trapezium ABCD with AB parallel to DC, E and F are the mid-points of the non-parallel sides AD and BC. Prove that EF is parallel to AB and equal to half the sum of AB and DC.
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Same chapter3 marksDifficulty: Medium
In triangle ABC, D and E are the mid-points of AB and AC. If BC = 12 cm, find DE.
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Same chapter2 marksDifficulty: Easy
State the mid-point theorem and its converse.
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Same chapter3 marksDifficulty: Medium
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