GFCP - Segments and Angles Lesson

Segment Addition

Given three collinear points,, how would you find the distance between the two endpoints?  You can use the Segment Addition Postulate!

The Segment Addition Postulate states that when you have three collinear points (points that are on the same line) as shown below, the distance AB + BC = AC.

 

Reading maps: Use the map to find the distances between the three cities that are collinear.

Given: The distance between Marietta and Atlanta is 20 miles. The distance between Atlanta and Macon is 85 miles.  Using the Segment Addition Postulate, the distance between Marietta and Macon is:

20 + 85 = 105 miles.

Segment Addition

Angle Addition

We can apply the same principles to adding angles. 

When there are two adjacent angles such that they share the same vertex and side (or ray) between each angle, then the sum of the angles is equal to the measure of the larger angle.  Here is an example.

$∠ABD+ ∠DBC= ∠ABC$

$34°+62°=96°$

 

Peripheral Vision:  In this image, the horse is wearing blinkers causing limited vision in each eye.  The angle of vision seen by both eyes have a measure of 75 degrees.  The angle of vision for each eye measures 110 degrees .  Find the angle of vision seen by the right eye alone.

Use the Angle Addition Postulate:

$m∠1+m∠2=110°$	Total vision for right eye is 110
$m∠1=110°-m∠2$	Subtract  from each side.
$m∠1=110°-75°$	Substitute 75 for
$m∠1=35°$	Subtract.

Therefore, the vision for the right eye alone measures $35°$.

Angle Addition

All images are free to use