Post on 21-Feb-2016
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Bell Ringer Activity:Pick your FAB FIVE….
This means pick the top 5 homework problems you want to work on.
5.5 Inequalities in Triangles
These triangles are NOT created equal……….
First, let’s review solving inequalitiesRules for solving:
We can add, subtract, multiply and divide both sides by by the same value JUST LIKE when we solve equationsEXCEPT
when we multiply or divide by a negative number.
Try these:
Corollary to the Triangle Exterior Angle Theorem
• A corollary is a result of another theorem.• If m<2 = 50 degrees and m<3 = 63 degrees,
what is the smallest degree measure that angle 1 could be?
Applying the theorem to problems
Show that m <2 > m <3:
By the Isosceles Triangle Theorem, we know that <1 is congruent to <2.
By the Triangle Exterior Angle Theorem, we know that m < 1 > m <3.
Since m <1 = m <2, then we use substitution to show that m < 2 > m < 3.
Applying the theorem to problems
Show that m <OTY > m <3:
Since m <OTY = m <4 + m <2, then m <OTY > m <2.
We also know that m < 3 > m <2.
So, since m <OTY > m <2 AND m < 2 > m <3 then m <OTY > m <3.
Sample Problems
If the length XZ > length YZ. Which is the larger angle, <X or <Y?
Sample Problems
• List the angles in order from least to greatest.
Theorem 5-11 is the converse of Theorem 5-10
REMINDER: To find the converse of a conditional statement, switch the hypothesis and the conclusion.
Apply Theorem 5-11
List the sides of the triangle from least to greatest.
Experiment & Discussion
• Take your pieces of paper and try to construct a triangle with them. What happens?
Triangle Inequality Theorem
How to apply the Triangle Inequality Theorem
Can a triangle have sides with the given lengths?
3 ft, 7 ft, 8 ft
Check to see that the sum of every pair of sides is greater than the third side:• 3 + 7 > 8• 8 + 7 > 3• 3 + 8 >7
Finding possible side lengths given two side lengths
• If a triangle has lengths of 8 ft and 12 ft, what are the possible lengths for a third side?
Multiple Choice Practice
Homework
• Bring in your Triangle with the Center of Gravity indicated on one side.
• Geometry 1st and 3rd:• Practice 5-5, pg 295 #36
• Geometry Honors:• Practice 5-5, evens, Enrichment 5-5, pg 295, #36