Basic Concepts
In a nutshell: Geometry helps you measure, compare, and visualize the world around you.
## Shapes, Angles, and Area
Geometry is about the properties and relationships of shapes. On the ACT, expect questions about triangles, circles, rectangles, and 3D figures.
### Angles
- The sum of angles in a triangle is always \( 180^\circ \).
- Perpendicular lines meet at \( 90^\circ \).
### Area and Perimeter
- Area of a rectangle: \( A = l \times w \)
- Area of a circle: \( A = \pi r^2 \)
- Perimeter is the distance around a shape.
### Volume
- For a box: \( V = l \times w \times h \)
### Real-World Connection
Geometry helps with everything from planning a garden to figuring out how much paint you need for a wall.
### Fun Fact
Circles have the smallest perimeter for a given area!
Examples
- Finding the area of a circle with radius 4: \( A = \pi \times 4^2 = 16\pi \)
- Calculating the perimeter of a rectangle with sides 3 and 7: \( 2 \times (3+7) = 20 \)