A
What is geometry mainly about?
Shapes, angles, area, and spatial reasoning
What does “area” measure?
The space inside a shape
What is symmetry?
A shape that can be folded into equal halves
What is decomposition in geometry?
Breaking a shape into smaller parts
What tool helps us “see hidden lines” in geometry problems?
Auxiliary lines
A square has side length 5 cm. What is its area?
25 cm²
What is the area formula of a rectangle?
length × width
What is the area of a triangle formula?
½ × base × height
What does “equal-area” mean?
Two shapes or parts have the same area
If a shape is cut into 2 equal parts, what is true about their areas?
They are equal
Does symmetry always mean equal area?
Yes (in most basic cases)
Does equal area always mean symmetry?
No
Why do we draw auxiliary lines?
To reveal hidden shapes or relationships
A square is split diagonally. What shapes are formed?
Two equal triangles
What is the key idea in equal-area problems?
Total area stays constant
Why is decomposition useful in geometry?
It simplifies complex shapes into known shapes
A shape is made of 3 squares. What strategy helps find area?
Split into individual squares
What happens when you draw a diagonal in a rectangle?
It creates two equal triangles
What is the main skill used in folded-paper problems?
Visualization
Why are geometric problems not solved by formula alone?
They require reasoning and visualization
A square has area 60 cm². What is its side length?
√60
Why might we NOT need to calculate side length in geometry puzzles?
Because relationships matter more than exact values
In equal-area reasoning, what is the key assumption?
Total area is preserved even after rearranging
A shape is split into parts using auxiliary lines. What is the main goal?
To create known shapes for calculation
Explain why drawing extra lines helps solve geometry problems.
It reveals hidden relationships and converts complex shapes into simpler ones