Q1
What is true about triangles with the same base and between the same parallels?
AThey have equal areas
BThey have equal perimeters
CThey are congruent
DThey have no relationship
ICSEClass 9 (ICSE)MathematicsCh 16 · Topic 2
Practice and Revision - Area Theorems (Proof and Use)
Let us practise and revise what we learned about area theorems (proof and use). Area theorems relate the areas of triangles and parallelogra
Core concept
Triangles with the same base and lying between the same parallel lines have equal areas, regardless of their exact shape.
How it works
A parallelogram and a triangle sharing the same base and lying between the same parallels have the parallelogram's area equal to twice the triangle's area.
Why it matters
These theorems can be proven using properties of congruent triangles and are useful for solving complex area problems.
Key detail
Understanding area theorems helps us calculate and compare areas without needing all specific measurements of a figure.
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Quick notes
• Same base, same parallels: triangles have equal area.
• This applies regardless of exact shape.
• Parallelogram area = 2 × triangle area (same base, same parallels).
• These theorems use congruent triangle properties.
• They're proven through geometric reasoning.
• They help solve complex area problems.
• They allow area comparison without all measurements.
• These are fundamental geometry theorems.