Geometry for Praxis II ParaPro Test Prep Study Guide (page 2)
The practice quiz for this study guide can be found at:
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.
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.
- 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.
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).
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 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.
- 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).
To find the perimeter of a figure, simply add up the lengths of all of its sides.
- 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.
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.
- 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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