- A13
- B24
- C12
- D11
Step-by-Step Solution
The segment joining the midpoints of the non-parallel sides of a trapezium equals half the sum of the parallel sides: EF = cm.
Answer: C) 12
A trapezium ABCD has AB ∥ DC. E and F are midpoints of the non-parallel sides AD and BC. If AB = 10 cm and DC = 14 cm, find EF (in cm).
Class 9QuadrilateralsGeometry — Quadrilaterals
Key idea: The mid-point theorem
**Theorem (Mid-Point)**: The line segment joining the mid-points of any two sides of a triangle is parallel to the third side and equal to half of it.
In ΔABC, let D be midpoint of AB and E be midpoint of AC. Then DE ∥ BC and DE = (1/2) × BC.
**Converse**: A line through the midpoint of one side parallel to another side will bisect the third.
In ΔABC, if D is midpoint of AB and a line through D parallel to BC meets AC at E, then E is the midpoint of AC.
**Use**: this theorem solves a huge class of problems where you have midpoints of triangle sides — you can immediately conclude parallelism and half-length.
In ΔABC, let D be midpoint of AB and E be midpoint of AC. Then DE ∥ BC and DE = (1/2) × BC.
**Converse**: A line through the midpoint of one side parallel to another side will bisect the third.
In ΔABC, if D is midpoint of AB and a line through D parallel to BC meets AC at E, then E is the midpoint of AC.
**Use**: this theorem solves a huge class of problems where you have midpoints of triangle sides — you can immediately conclude parallelism and half-length.
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