Same chapter3 marksDifficulty: Medium
In triangle ABC, D, E and F are the mid-points of BC, CA and AB. If the perimeter of ABC is 24 cm, find the perimeter of triangle DEF.
Mid-point Theorem
3 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.
Original Khojo Papers practice question — not from a past board paper.
Answer
Join DF and produce it to meet AB produced at G. Triangles DFC and GFB are congruent by ASA, so DC = BG and DF = FG. In triangle ADG, E and F are the mid-points of AD and DG, so by the mid-point theorem EF is parallel to AG and equal to half of it, that is half of AB + BG = AB + DC.
No citable source has been recorded for this record. Treat it as practice material, not as fact.
Explanation
EF is called the median or mid-segment of the trapezium.
Related questions
From the same topic and chapter, at a similar level.
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