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5.3 Inequalities in One Triangle ink.notebook
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December 06, 2016
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5.3 Inequalities
in One Triangle
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5.3 Inequalities in One Triangle ink.notebook
December 06, 2016
Lesson Objectives
Lesson Objectives
Standards
Standards
Lesson Notes
Lesson Notes
5.3 Inequalities in One Triangle
After this lesson, you should be able to successfully compare side lengths and angles of triangles.
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Lesson Objectives
Standards
Lesson Notes
G.CO.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).
G.C.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.
G.CO.10 Prove theorems about triangles.
G.GPE.6 Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
Example 1
Mark the largest angle, longest side, smallest angle, and shortest side of the triangle shown below.
The longest side and largest angle are ____________ each other.
The shortest side and smallest angle are ____________ each other. 2
5.3 Inequalities in One Triangle ink.notebook
Example 2
List the sides of ∆PQR in order from shortest to longest.
December 06, 2016
Q
80¡
P
45¡
55¡
R
Exterior Angle Theorem
If an angle is an exterior angle of a triangle, then its measure is ___________ than the measure of either of its corresponding remote interior angles.
mÚ4 > ________ 2
and mÚ4 > ________ 1
3
4
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5.3 Inequalities in One Triangle ink.notebook
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Example 3: List all angles of ΔEFG whose measures are less than mÚ1.
The measure of an exterior is greater than the measure of either remote interior angles. mÚ_____ < mÚ1 and mÚ_____ < mÚ1 Use the Exterior Angle Inequality Theorem to list ALL of the angles that satisfy the stated condition.
1. Measures are less than mÚ1 2. Measures are greater than mÚ4
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5.3 Inequalities in One Triangle ink.notebook
Use the Exterior Angle Inequality Theorem to list ALL of the angles that satisfy the stated condition.
December 06, 2016
Use the Exterior Angle Inequality Theorem to list ALL of the angles that satisfy the stated condition.
3. Measures are less than mÚ1 6. Measures are greater than mÚ3
4. Measures are greater than mÚ1
7. Measures are greater than mÚ5
5. Measures are less than mÚ7 8. Measures are less than mÚ4 When the sides of triangles are not congruent, there is a relationship between the sides and angles of the triangles.
If one side of a triangle is longer than another side, then the angle opposite the longer side is __________ than the angle opposite the shorter side.
B
8
5
A
AB > BC, So m ∠ ____ > m ∠ ____ .
C
If one angle of a triangle is larger than another angle, then the side opposite the larger angle is ___________ than the side opposite the smaller angle.
B
A
50¡
m ∠ A > m ∠ C, So _____ >_____.
30¡
C
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5.3 Inequalities in One Triangle ink.notebook
December 06, 2016
Example 4
List the angles in order from smallest to largest
measure.
∠ ____ , ∠ ____ , ∠ ____ Example 5
List the sides in order from shortest to longest
measure.
_____, _____, _____
List the angles AND sides in order from smallest to largest.
9.
∠ ____ , ∠ ____ , ∠ ____ _____, _____, ______
10.
∠ ____ , ∠ ____ , ∠ ____ _____, _____, ______
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5.3 Inequalities in One Triangle ink.notebook
December 06, 2016
List the angles AND sides in order from smallest to largest.
11.
∠ ____ , ∠ ____ , ∠ ____ _____, _____, ______
12.
∠ ____ , ∠ ____ , ∠ ____ _____, _____, ______
PRACTICE
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5.3 Inequalities in One Triangle ink.notebook
Use the Exterior Angle Inequality Theorem to list ALL of the angles that satisfy the stated condition.
December 06, 2016
List the angles and sides in order from smallest to largest.
5.
6.
1. Measures are less than mÚ1 2. Measures are less than mÚ9 3. Measures are greater than mÚ5
∠ ____ , ∠ ____ , ∠ ____ 4. Measures are greater than mÚ8
_____, _____, ______
List the angles and sides in order from smallest to largest.
7.
∠ ____ , ∠ ____ , ∠ ____ _____, _____, ______
8.
∠ ____ , ∠ ____ , ∠ ____ _____, _____, ______
∠ ____ , ∠ ____ , ∠ ____ _____, _____, ______
List the angles and sides in order from smallest to largest.
9.
∠ ____ , ∠ ____ , ∠ ____ _____, _____, ______
10.
∠ ____ , ∠ ____ , ∠ ____ _____, _____, ______
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5.3 Inequalities in One Triangle ink.notebook
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Use the figure at the right to determine which angle has the greatest measure.
Use the figure at the right to determine the relationship between the measures of the given angles.
11. Ú1, Ú3, Ú4 15. mÚQRW _____ mÚRWQ 12. Ú4, Ú8, Ú9 16. mÚRTW _____ mÚTWR 13. Ú2, Ú3, Ú7 17. mÚRTS _____ mÚTRS 14. Ú7, Ú8, Ú10 18. mÚWQR _____ mÚQRW Use the figure at the right to determine the relationship between the lengths of the given sides.
23. The figure shows the position of three trees on one part of a Frisbee course. At which tree position is the angle between the trees the greatest?
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5.3 Inequalities in One Triangle ink.notebook
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Answers:
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