Same chapter3 marksDifficulty: Medium
Prove that a parallelogram and a triangle on the same base and between the same parallels have areas in the ratio 2 : 1.
Area Theorems
3 marksDifficulty: Medium
Prove that a median of a triangle divides it into two triangles of equal area.
Original Khojo Papers practice question — not from a past board paper.
Answer
The median joins a vertex to the mid-point of the opposite side, so the two triangles formed have equal bases and the same height, the perpendicular from that vertex to the base. Since area is half base times height, the two areas are equal.
No citable source has been recorded for this record. Treat it as practice material, not as fact.
Explanation
It follows that the three medians divide a triangle into six triangles of equal area.
Related questions
From the same topic and chapter, at a similar level.
Same chapter1 markDifficulty: Medium
Triangles on the same base and between the same parallels are:
Area Theorems
Same chapter3 marksDifficulty: Medium
ABCD is a parallelogram of area 48 cm2. Find the area of triangle ABC.
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Same chapter3 marksDifficulty: Medium
State the relation between the area of a triangle and that of a parallelogram on the same base and between the same parallels.
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Same chapter2 marksDifficulty: Easy
State the theorem about the areas of parallelograms on the same base and between the same parallels.
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Same subject3 marksDifficulty: Medium
Factorise x4 − 81.
Factorisation