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