Trigonometry & Inverse Trigonometry
Triangle Properties
Grade 11
Question:
<p>D, E and F are the middle points of the sides of the triangle ABC, then</p>
<p>(a) centroid of the triangle DEF is the same as that of ABC</p>
<p>(b) orthocentre of the triangle DEF is the circumcentre of ABC</p>
<p>(c) orthocentre of the triangle DEF is the incentre of ABC</p>
<p>(d) centroid of the triangle DEF is not the same as that of ABC</p>
Step-by-Step Solution
Key Concept: The medial triangle shares the same centroid as the original triangle because the centroid is determined by the average position of vertices.
<p>The medial triangle DEF (formed by midpoints of sides) has the same centroid as the original triangle ABC. This is because the centroid divides each median in the ratio 2:1 from vertex, and the midpoint configuration preserves this property.</p>
Correct Answer: A