- A12
- B24
- C11
- D13
Step-by-Step Solution
Each side of ΔDEF (the medial triangle) equals half of a side of ΔABC by the mid-point theorem. So its perimeter = cm.
Answer: A) 12
In ΔABC, D, E, F are midpoints of BC, CA, AB. If the perimeter of ΔABC is 24 cm, find the perimeter of ΔDEF (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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