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: