2022 · Q78
Let D, E and F be the midpoints of the sides BC, CA and AB respectively of a triangle ABC. Triangle DEF is congruent to which of the following triangles?
- 1AEF
- 2FBD
- 3EDC
Select the correct answer using the code given below.
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A1 only
- B2 and 3 only
- C3 only
- D1, 2 and 3
Explanation
D, E, F being midpoints, the mid-segment theorem gives FE = BC/2, FD = AC/2, DE = AB/2. Thus each of AEF, FBD, EDC has sides AB/2, AC/2, BC/2, exactly the sides of DEF - all four are mutually congruent by SSS. Key disputed: a widely circulated third-party Set-A key lists B, but AEF ≅ DEF as well. Hence the keyed option is D.