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

The practice quiz for this study guide can be found at:

Math for Praxis II ParaPro Test Prep Practice Problems

The ParaPro Assessment will test your knowledge of basic shapes, such as triangles and circles, and it will also ensure that you remember how to identify points on the coordinate plane.

Polygons

A polygon is a two-dimensional object with straight lines that create a closed figure.

• A regular polygon has sides with the same lengths, and congruent angles with the same measures.
• An irregular polygon does not have sides with the same lengths and congruent angles with the same measures.

You should be prepared to identify the following polygons:

A triangle is a polygon with 3 sides.

A quadrilateral is a polygon with 4 sides.

A pentagon is a polygon with 5 sides.

A hexagon is a polygon with 6 sides.

An octagon is a polygon with 8 sides.

There are special kinds of triangles that are important to know.

An equilateral triangle has three sides with the same length.

An isosceles triangle has two sides with the same length.

A scalene triangle has no sides with the same length.

There are also special kinds of quadrilaterals that are important to know.

A rectangle is a four-sided polygon with four right angles. All rectangles have two pairs of parallel sides.

A square is a four-sided polygon with four right angles and four equal sides. All squares have two pairs of parallel sides. Note that a square is a specific kind of rectangle.

Example

What type of shape is shown below?

Because the figure has straight lines and makes a closed figure, it is a polygon. Because there are exactly five straight lines, the figure is a polygon.

Circles

A circle is a curved, two-dimensional figure where every point on the circle is the same distance from the center.

There are several parts of a circle that you should know.

The diameter is a line that goes directly through the center of a circle—the longest line segment that can be drawn in a circle.

The radius is a line segment from the center of a circle to a point on the circle (half of the diameter).

Area

The area is the amount of space inside a two-dimensional shape.

To find the area of a rectangle, you need to multiply the length of the rectangle times the width. The formula is area = length × width, or area = lw.

To find the area of a triangle, you need to multiply times the base of the triangle times its width. The formula is area = base × width, or area = ()lw.

To find the area of a circle, you need to multiply the radius by itself (or square it), and then multiply it by π. The formula is area = πr², where r is the radius of the circle.

Example

What is the area of the following rectangle?

To find the area of a rectangle, multiply the length by the height. Because the length is 12 and the height is 5, the area is therefore 12 ×5, or 60 square units.

Example

What is the area of the following triangle?

The base of the triangle is 8 and its height is 5. To find the area, just plug in those known values into the formula area = lw. You will get area = (8)(5), which is equal to 20. The area is 20 square units.

Example

What is the area of a circle with a radius of 2?

Plug in the value of the radius into the formula for the area of a circle: area = πr². You will get area = π2², which is equal to 4π.

Volume

Volume is the amount of space inside a three-dimensional shape. To find the volume of a rectangular solid, you need to multiply the length times the width times the height.

Example

What is the volume of the following cube?

To find the volume, you need to multiply the length times the width times the height. Each dimension of the cube is 4, so the volume is 4 ×4 ×4, or 64 cubic units.

The practice quiz for this study guide can be found at:

Math for Praxis II ParaPro Test Prep Practice Problems