HONORS GEOMETRY 5.3. Inequalities in One Triangle

Do Now: Welcome Back! Complete the Do Now given to you when you walked into class today Think or =

Reminder: Inequalities involve either: A greater than sign ( > ) OR A less than ( < ) sign

Definition of Inequality For any real numbers a and b, a>b if and only if there is a positive number c such that a = b+c. Ex: If 5= then 5>2 and 5>3

Recall: Interior Angles? Exterior Angles? Remote Interior angles? What does the exterior angle theorem claim?

So….

Exterior Angle Inequality

Example One:

Example Two:

You Try!

Triangle Relationship: In a triangle, the smallest angle is opposite the smallest side the largest angle is opposite the largest side

Example Three:

Example Four:

You Try!

2 theorems: If one side of a triangle is longer than another side, then the angle opposite the longer side has a greater measure than the angle opposite the shorter side. If one angle of a triangle has a greater measure than another angle, then the side opposite the greater angle is longer than the side opposite the smaller angle.

Example Five:

Example Six:

You Try!

Practice Problems Try some on your own/in your table groups As always don’t hesitate to ask me and or your tablemates questions if you are confused.

Exit Ticket: