Transcript Lesson 5-2A PowerPoint

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Lesson 5-1 Bisectors, Medians, and Altitudes
Lesson 5-2 Inequalities and Triangles
Lesson 5-3 Indirect Proof
Lesson 5-4 The Triangle Inequality
Lesson 5-5 Inequalities Involving Two Triangles
Example 1 Compare Angle Measures
Example 2 Exterior Angles
Example 3 Side-Angle Relationships
Example 4 Angle-Side Relationships
Determine which angle has the greatest measure.
Explore Compare the measure of 1 to the measures
of 2, 3, 4, and 5.
Plan
Use properties and theorems of real numbers
to compare the angle measures.
Solve
Compare m3 to m1.
By the Exterior Angle Theorem,
m1 m3 m4. Since angle measures
are positive numbers and from the definition
of inequality, m1 > m3.
Compare m4 to m1.
By the Exterior Angle Theorem, m1 m3 m4.
By the definition of inequality, m1 > m4.
Compare m5 to m1.
Since all right angles are congruent, 4 5.
By the definition of congruent angles, m4 m5.
By substitution, m1 > m5.
Compare m2 to m5.
By the Exterior Angle Theorem, m5 m2 m3.
By the definition of inequality, m5 > m2.
Since we know that m1 > m5, by the
Transitive Property, m1 > m2.
Examine The results on the previous slides show that
m1 > m2, m1 > m3, m1 > m4, and
m1 > m5. Therefore, 1 has the greatest
measure.
Answer: 1 has the greatest measure.
Determine which angle has the greatest measure.
Answer: 5 has the greatest measure.
Use the Exterior Angle Inequality Theorem to list all
angles whose measures are less than m14.
By the Exterior Angle Inequality Theorem, m14 > m4,
m14 > m11, m14 > m2, and m14 > m4 + m3.
Since 11 and 9 are vertical angles, they have equal
measure, so m14 > m9. m9 > m6 and m9 > m7,
so m14 > m6 and m14 > m7.
Answer: Thus, the measures of 4, 11, 9,  3,  2, 6,
and 7 are all less than m14 .
Use the Exterior Angle Inequality Theorem to list all
angles whose measures are greater than m5.
By the Exterior Angle Inequality Theorem, m10 > m5,
and m16 > m10, so m16 > m5, m17 > m5 + m6,
m15 > m12, and m12 > m5, so m15 > m5.
Answer: Thus, the measures of 10, 16, 12, 15 and
17 are all greater than m5.
Use the Exterior Angle Inequality Theorem to list all of
the angles that satisfy the stated condition.
a. all angles whose measures are less than m4
Answer: 5, 2, 8, 7
b. all angles whose measures are greater than m8
Answer: 4, 9, 5
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