Let ABC be a triangle. If the mid-points of AB, BC and AC are D, E and F, respectively, then ∆DEF is NOT congruent to _____.
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. ∆ABC.
The mid-points of AB, BC, and AC are D, E, and F, respectively.
∆DEF is formed by the midpoints D, E, and F of the sides AB, BC, and AC of triangle ∆ABC.
The midpoints divide ∆ABC into smaller triangles, specifically congruent triangles.
By the midpoint theorem, ∆DEF is similar to ∆ABC but not congruent to ∆ABC due to size differences.
∆DEF will be congruent to smaller triangles such as ∆BDE, ∆ECF, and ∆ADF since they have identical side lengths and angles.
Therefore, ∆DEF is not congruent to ∆ABC.