Geometry Section 5-3 11-12

SECTION 5-3Inequalities in One Triangle

Tuesday, March 6, 2012

ESSENTIAL QUESTIONS

How do you recognize and apply properties of inequalities to the measures of the angles of a triangle?

How do you recognize and apply properties of inequalities to the relationships between the angles and sides of a triangle?


VOCABULARY

1. Inequality:


VOCABULARY

1. Inequality: For any real numbers a and b, a > b IFF there is a positive number c such that a = b + c


PROPERTIES OF INEQUALITY FOR REAL NUMBERS

1. Comparison Property of Inequality:

2. Transitive Property of Inequality:

3. Addition Property of Inequality:

4. Subtraction Property of Inequality:



1. Comparison Property of Inequality: a < b, a = b, a > b

2. Transitive Property of Inequality:






2. Transitive Property of Inequality: If a < b and b < c, then a < c; If a > b and b > c, then a > c







3. Addition Property of Inequality: If a < b, then a + c < b + c; If a > b, then a + c > b + c






3. Addition Property of Inequality: If a < b, then a + c < b + c; If a > b, then a + c > b + c

4. Subtraction Property of Inequality: If a < b, then a − c < b − c; If a > b, then a − c > b − c


THEOREMS

5.8 - Exterior Angle Inequality: The measure of an exterior angle of a triangle is greater than the measure of either of its corresponding remote interior angles


ANGLE-SIDE RELATIONSHIPS IN TRIANGLES

5.9: If one side of a triangle is longer than another side, then the angle oppostie the longer side has a greater measure than the angle opposite the shorter side

5.10: If one angle of a triangle has a greater measure than another angle, then the side oppostie the larger angle has a greater measure than the side opposite the smaller angle


EXAMPLE 1

Use the Exterior Angles Inequality to list all of the angles that satisfy the stated condition.

a. Measures less than m∠14

b. Measures greater than m∠5


EXAMPLE 1


a. Measures less than m∠14∠7, ∠12, ∠1, ∠8, ∠10,

∠4, ∠5



EXAMPLE 1


a. Measures less than m∠14∠7, ∠12, ∠1, ∠8, ∠10,

∠4, ∠5


∠10, ∠16, ∠12, ∠14, ∠15


EXAMPLE 2

List the angles of ∆ABC in order from smallest to largest.


EXAMPLE 2

List the angles of ∆ABC in order from smallest to largest.

∠C, ∠A, ∠B


EXAMPLE 3

List the sides of ∆ABC in order from shortest to longest.


EXAMPLE 3

List the sides of ∆ABC in order from shortest to longest.

AC, AB, BC


EXAMPLE 4

Ebony is following directions for folding a handkerchief to make a bandana for her hair. After she folds the handkerchief in half, the directions

tell her to tie the two smaller angles of the triangle under her hair. If she folds the

handkerchief with the dimensions shown, which two ends should she tie?


EXAMPLE 4

Ebony is following directions for folding a handkerchief to make a bandana for her hair. After she folds the handkerchief in half, the directions

tell her to tie the two smaller angles of the triangle under her hair. If she folds the

handkerchief with the dimensions shown, which two ends should she tie?

∠Y and ∠Z should be tied, as they are the smallest angles (opposite

shortest sides)Tuesday, March 6, 2012

CHECK YOUR UNDERSTANDING

Review problems #1-7 on p. 346


PROBLEM SET


PROBLEM SET

p. 346 #9-37 odd, 45, 53, 57

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Geometry Section 5-3 11-12

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