Sections 1.4 and 1.5 Brit Caswell.

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Presentation transcript:

Sections 1.4 and 1.5 Brit Caswell

An angle is formed by two rays with the same endpoint. The rays are the sides of the angle The endpoint is the vertex of the angle

Naming an Angle To name an angle, you use the angle symbol followed by three points of the angle. The middle point will always be the vertex of the angle. It is also possible to name an angle according to a variable. The most common angle names are…

The unit of measurement of an angle is usually degrees The unit of measurement of an angle is usually degrees. Some mathematicians use another unit called radians. In this class, we will discuss degrees. Example:

The measure of an angle is the absolute value of the distance between the legs of the angle. We use the measure of the angle to determine the type of angle that is being studied. This is the format to write measure:

Acute Angles Acute Angles measure less than 90˚.

Right Angles Right Angles measure exactly 90˚.

Obtuse Angles Obtuse Angles measure more than 90˚.

Straight Angles Straight Angles measure exactly 180˚.

Angles with the same measure are called…

Postulate 1.8 Angle Addition Postulate Angles can be added together in the same way as segments.

Adjacent Angles Adjacent angles are two coplanar angles with a common side, a common vertex, and no common interior points.

Vertical Angles Vertical angles are two angles whose sides are opposite rays.

Complementary Angles Complementary angles are two angles whose measures have a sum of 90. Each angle is called the complement of the other.

Supplementary Angles Supplementary angles are two angles whose measures have a sum of 180. Each angle is called the supplement of the other.

Postulate 1.9 Linear Pair Postulate If two angles form a linear pair, they are supplementary.

Proof: Vertical Angles are Congruent

I Do <KPL and <JPL are a linear pair. What are the measures of <KPL and <JPL? L 2x+24 4x+36 P J K

We Do (Popcorn) (Pg. 37) Name a pair of the following types of angle pairs. 1. Vertical 2. complementary 3. Linear pair E A F B C D

You Do (Exit Ticket) Determine the sets of angular pairs within the bottom image. 12 11 10 1 2 8 9 5 4 6 3 7