- A9 cm
- B14 cm
- C28 cm
- D8 cm
Step-by-Step Solution
In is the mid-point of and , so is the mid-point of and cm. In is the mid-point of and , so cm. Hence cm.
Answer: B) 14 cm
ABCD is a trapezium with AB ∥ DC, AB = 18 cm and DC = 10 cm. E is the mid-point of AD, and the orange line EF is drawn parallel to AB to meet BC at F. The dashed diagonal AC cuts EF at G. Find EF.
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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