Basic Geometry
1. Define area.
Area accounts for the whole space.
2. Define perimeter.
Perimeter is the entire length of the boundary.
3. Define polygon.
Plane figure that is described by a finite number of straight line (no curve sides) segments connected to form a closed polygonal chain
4. Define a regular polygon.
Regular - equal sides and angles
5. Define perpendicular lines.
Two lines intersect at right angles. All sides have 90 degrees.
6. Define parallel lines.
The lines will not intersect and will have the same distance between them.
7. Define the area of the parallelogram.
Base x Height
8. Define the area of triangle.
0.5 x Base x Height
9. Define circle.
A circle is where the lines from the center to the outer point have equal distances from the center.
10. Provide the definitions of circle’s radius and diameter and circumference.
- Radius: Distance from the outer point from the center point.
- Diameter: 2 x Radius
- Circumference: The perimeter of the circle (distance around the circle)
11. Provide the formula to calculate circle’s circumference.
$2.π.r$
12. Provide the formula to calculate the area of the circle.
$π.r^2$
13. Provide the formula of $\pi$.
$\pi = \frac{\text{Circumference}}{\text{Diameter}}$
14. Provide the formula to calculate a cylinder volume.
$h.π.r^2$
15. Explain translation transformation, provide an example and the mathematical representation.
- Translation: A translation moves a figure in a straight line by a certain distance.
- Representation: Translation is represented by a vector that gives the direction and distance of the translation. For example, the translation that moves a figure 2 units to the right and 3 units up can be represented by the vector (2, 3).
16. Explain rotation transformation, provide an example and the mathematical representation.
- Rotation: A rotation turns a figure around a fixed point by a certain angle.
- Representation: A rotation is represented by an angle and a point. The angle is the amount of rotation, and the point is the center of rotation. For example, a rotation of 90 degrees clockwise around the origin can be represented by the angle 90 and the point (0, 0).
17. Explain dilation transformation, provide an example and the mathematical representation.
- Dilation: A dilation enlarges or shrinks a figure by a certain factor.
- Representation: A dilation is represented by a scale factor. The scale factor is the amount by which the figure is enlarged or shrunk. For example, a dilation with a scale factor of 2 enlarges the figure by a factor of 2.
18. Explain reflection transformation, provide an example and the mathematical representation.
- Reflection: A reflection flips a figure over a line.
- Representation: A reflection is represented by a line. The line is called the mirror line. For example, a reflection across the x-axis can be represented by the line x = 0.