9.2 Angle Classification
Learning Objectives
- I can classify angles based on their angle measure.
Introduction
What if you were given the degree measure of an angle? How would you describe that angle based on its size? After completing this Concept, you'll be able to classify an angle as acute, right, obtuse, or straight.
Guided Learning
Angles can be grouped into four different categories.
Straight Angle: An angle that measures exactly .
Acute Angles: Angles that measure between and up to but not including .
Obtuse Angles: Angles that measure more than but less than .
Right Angle: An angle that measures exactly .
This half-square marks right, or , angles. When two lines intersect to form four right angles, the lines are perpendicular. The symbol for perpendicular is .
This figure is made by intersecting lines, lines that cross one another. Even though all four angles are , only one needs to be marked with the half-square. is read is perpendicular to line .
This figure in also made by intersecting lines. Congruent opposite angles that are formed by intersecting lines are called vertical angles. In this figure, angles a and b are vertical angles which means they are congruent.
Example A
What type of angle is ?
is less than , so it is acute.
Example B
Name the angle and determine what type of angle it is.
The vertex is . So, the angle can be or . To determine what type of angle it is, compare it to a right angle.
Because it opens wider than a right angle and is less than a straight angle, it is obtuse.
Example C
What type of angle is ?
is greater than , but less than , so it is obtuse.
Guided Practice
Name each type of angle:
1.
2.
3.
Check your answers with a partner.
Solutions
1. Right
2. Acute
3. Straight
Review
- Angles can be classified by their measurements.
Straight angle
A straight angle is an angle that measures exactly .
Acute angles
Acute angles are angles that measure between and up to but not including .
Obtuse angles
Obtuse angles are angles that measure more than but less than .
Right angle
A right angles is an angle that measures exactly .
Perpendicular
When two lines intersect to form four right angles they are called perpendicular. The symbol for perpendicular is .
Intersecting lines
Intersecting lines are lines that cross one another.
Vertical angles
Vertical angles are congruent angles that are formed by intersecting lines and are directly opposite
of each other.