Page 133 - Math Course 2 (Book 2)

Triangle Properties of Inequalities
Mo. 10

Lesson 4 Explore Compare the measure of ∠1 to the
measures of ∠2, ∠3, ∠4, and ∠5.

Plan Use properties and theorems of real
KEY CONCEPTS: numbers to compare the angle
measures.
1. Recognize and apply properties of
inequalities to the measures of angles Solve Compare m∠3 to m∠1.
of a triangle. By the Exterior Angle Theorem,
2. Recognize and apply properties of m∠1 = m∠3 + m∠4. Since angle
inequalities to the relationships between measures are positive numbers and
angles and sides of a triangle. from the definition of inequality,
m∠1 > m∠3.
Compare m∠4 to m∠1.
MO. 10 - L4a By the Exterior Angle Theorem,
m∠1 = m∠3 + m∠4. By the definition
Measures of Angles of inequality, m∠1 > m∠4.
of a Triangle Compare m∠5 to m∠1.
Since all right angles are congruent,
∠4 ≅ ∠5.
THEOREM 10.7 By the definition of congruent angles,
m∠4 = m∠5.
Exterior Angle in Enequaility By the substitution, m∠1 > m∠5.

If an angle is an exterior angle of a triangle, then its Compare m∠2 to m∠5.
measure is greater than the measure of either of its By the Exterior Angle Theorem,
corresponding remote interior angles. m∠5 = m∠2 + m∠3.
Example m∠4 > m∠1 B By the definition of inequality,
m∠5 > m∠2.
m∠4 > m∠2
2 Since we know that m∠1 > m∠5, by
the
Transitive Property, m∠1 > m∠2.
Examine The results of the previous slides
show that m∠1 > m∠2, m∠1 > m∠3,
1 3 4 m∠1 > m∠4, and m∠1 m∠5. Therefore,
A C ∠1 has the greatest measure.

Let’s Begin Answer ∠1 has the greatest measure.

Compare Angle Measures Exterior Angles

Example Examples

Determine which angle has the greatest measure. Use the Exterior Angle Inequality Theorem to list all
angles whose measures are less than m∠14.
14
5 17
16 4 5 6 15
4 3 11
10 12
3 2 1 2 1 9 8 7

125