skip navigation

lesson tab active practice tab inactive assignment tab inactive

1.07 Exploring Angles

 

 Blueprints for this Lesson:
 
  • Review the parts of an angle and how to name them.
  • Classify angles based on their measurement.

Foundational Knowledge:

An angle is a figure consisting of two rays with a common endpoint.

Angles are made up of two main parts:

  • Two sides formed by rays.
  • The common endpoint where the two rays meet is called the vertex.

Acute angle A B C with vertex at point B. It is also labeled as angle 1.

Sides: Ray B A and Ray B C
Vertex: point B

There are several ways to name this angle.

  • Using three letters: Angle A B C, Angle C B A
    Notice that the vertex is always listed in the middle of the three letters.
  • Using one letter: angle B
  • Using a number: angle 1
Framework For Understanding:

Have you ever looked at a structure to determine why it was pleasing to the eye? If you have, perhaps you noticed that some types of angles provide a more pleasing structure. Did you know that the more pleasing structure may have a higher cost? Some types of angles are not generally used in places where support is needed and therefore the architect must reinforce those angles with more expensive materials. Let's look closely at the types of angles and how we name them in Geometry.

Term Measure Picture and Name
Acute Acute angles measure between 0° and 90°
0° < m angle O < 90°

Reading Tips icon		 Acute angle D O T
We could call this Angle O, Angle D O T, or Angle T O D.
Right Right angles measure exactly 90°
m angle A = 90°

Reading Tips icon		 Right angle T A N
We place a little box in the corner to indicate the angle is a right angle.

We could call this angle A, Angle T A N, or Angle N A T.
Obtuse Obtuse angles measure between 90° and 180°
90° < m angle A < 180°

Reading Tips icon		 Obtuse angle R A T
We could call this Angle A, Angle R A T, or Angle T A R.
Straight Straight angles measure exactly 180°
m = 180°		 Straight angle D O G
This is angle of D O G, but you will typically see it as line l or Line G D. .

 

Perpendicular Lines

When two lines form to make right angles, we call them perpendicular. We use a symbol that looks like an upside down" T " for the word perpendicular.

Rays and segments can be perpendicular too. Here is a look at two perpendicular rays that form a right angle.

If : Ray A T is perpendicular to ray A N.

Then : The measure of angle T A N is equal to 90 degrees.

Reading Tips icon

 

 Right angle T A N. Angle A is a 90 degree angle. Ray A T is perpendicular to ray A R,

In the image to the right, line n is perpendicular to line p.
We can write this:

Line n is perpendicular to line p

 Line n is drawn perpendicular to line p. These lines form a right angle at their intersection.
Reminders

If more than one angle is formed at any vertex point, it is important that you name the angle using three letters, not just one.

Example: In the picture to the right, the angle that is in bold could be named Angle A B D or Angle D B A, but could not be named Angle B because vertex B belongs to more than one angle.

 

 Adjacent acute angles A B D and D B C. Ray B D is a shared side. The sum of the two acute angles is acute angle A B C.

An angle divides a plane into three distinct parts:

  1. The interior of the angle.

    D is in the interior of the angle.

  2. The exterior of the angle.

    B and F are in the exterior of the angle.

  3. The angle itself.

    C, A, and E are on the angle itself.
 Acute angle C A E. Point D is in the interior of the angle C A E. Points F, and B are in the exterior of the angle.

Take a few minutes and go on a Dynamic Exploration of Angles. Follow the directions on the page to explore different types of angles.

Now you are ready to move on to some practice with angles.