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# Geometry for Praxis II ParaPro Test Prep Study Guide (page 2)

By LearningExpress Editors
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### Three-Dimensional Shapes

You may be expected to identify some three-dimensional shapes on the ParaPro Assessment. The two most common types of three-dimensional shapes are shown below.

A cube is a three-dimensional figure where each face is the shape of a square.

A rectangular prism is a three-dimensional figure where each face is the shape of a rectangle. Note that a cube is a specific kind of rectangular prism.

### Coordinate Geometry

Coordinate geometry is a form of geometrical operations in relation to a coordinate plane. A coordinate plane is a grid created by a horizontal x-axis and a vertical y-axis.

These two axes intersect at one coordinate point, (0, 0), the origin. A coordinate point, also called an ordered pair, is a specific point on the coordinate plane with the first number representing the horizontal placement and the second number representing the vertical placement. Coordinate points are given in the form of (x, y).

### Graphing Ordered Pairs (Points)

The x-coordinate is listed first in the ordered pair and tells you how many units to move to either the left or the right. If the x-coordinate is positive, move to the right. If the x-coordinate is negative, move to the left.

The y-coordinate is listed second and tells you how many units to move up or down. If the y-coordinate is positive, move up. If the y-coordinate is negative, move down.

Example
What is the ordered pair of point X on the following coordinate grid?

The point on the grid is 3 units to the right of the origin. Therefore, the first number in the ordered pair is 3.

The point on the grid is 2 units down from the origin. Therefore, the second number in the ordered pair is –2.

The ordered pair for point X is (3, –2).

### Perimeter

To find the perimeter of a figure, simply add up the lengths of all of its sides.

Example
What is the perimeter of the following triangle?

The triangle has side lengths of 5, 8, and 10. The perimeter is therefore the sum of 5 + 8 + 10. The perimeter of the triangle is 23.

### Circumference

The circumference is the distance around a circle. The circumference can be found by multiplying the diameter of the circle by pi, or π, a special number equal to about 3.14. It can also be found by multiplying the radius of the circle by 2 and then by π. The formulas for the circumference of a circle are circumference = 2πr and circumference = dπ, where r is the radius and d is the diameter of the circle.

Example
What is the circumference of a circle with a radius of 5?
Following the formula area = 2πr, the circumference is equal to 2(5) π, which is equal to 10π

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