5.3 inequalities in one triangle objectives : recognize and apply properties of inequalities to the...
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5.3 5.3 Inequalities in One TriangleInequalities in One Triangle
ObjectivesObjectives::• Recognize and apply properties of Recognize and apply properties of
inequalities to the measures of the inequalities to the measures of the angles of a triangle.angles of a triangle.
• Recognize and apply properties of Recognize and apply properties of inequalities to the relationships inequalities to the relationships between the angles and sides of a between the angles and sides of a triangle.triangle.
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ConceptConcept
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Example 1Example 1
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Example 2Example 2
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Practice #1Practice #1
A.
B.
C.
D.
A.
B.
C.
D.
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Practice #2Practice #2
A.
B.
C.
D.
A.
B.
C.
D.
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5 7
835˚80˚
65˚
20˚
75˚ 85˚
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5.5
ConceptConcept
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What is the largest angle of the given triangle?
B
CA
5.5
5 7
9
Example 3Example 3
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Practice #3Practice #3
A. X, T, V
B. X, V, T
C. V, T, X
D. T, V, X
List the angles of ΔTVX in order from smallest to largest.
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List the sides from largest to smallest.
5.5
FE
D
110°
46°
A. DE, EF, DF
B. EF, DE, DF
C. DE, DF, EF
D. DF, DE, EF
Practice #4Practice #4
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A triangle is formed by three kitchen appliances as shown in the figure. The distances shown are measured in feet. What is wrong with the labels?
5.5
50°
60°
70°
10
6
8
refrigerator
sink
range
Practice #5Practice #5
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5.6 5.6 Inequalities in Two TrianglesInequalities in Two Triangles
ObjectivesObjectives::• Apply the Hinge Theorem or its Apply the Hinge Theorem or its
converse to make comparisons in two converse to make comparisons in two triangles.triangles.
• Prove triangle relationships using the Prove triangle relationships using the Hinge Theorem or its converse.Hinge Theorem or its converse.
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Think about this…Think about this…
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ConceptConcept
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Complete the inequality (or equation):
Example 4Example 4
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Complete the equation or inequality:3) m<1 ___ m<2 4) MS ____ LS 5) m<1 ____ m<2
Example 4Example 4
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Practice #6Practice #6
A. FG > GH
B. FG < GH
C. FG = GH
D. not enough information
A. Compare the lengths of FG and GH.
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Practice #7Practice #7
A. mJKM > mKML
B. mJKM < mKML
C. mJKM = mKML
D. not enough information
B. Compare mJKM and mKML.
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Practice #8Practice #8
A. Meena’s kite
B. Rita’s kite
Meena and Rita are both flying kites in a field near their houses. Both are using strings that are 10 meters long. Meena’s kite string is at an angle of 75° with the ground. Rita’s kite string is at an angle of 65° with the ground. If they are both standing at the same elevation, which kite is higher in the air?
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Warm UpWarm Up
Use the Exterior Angle Inequality Theorem to:
a)List the angles that are greater than m<2
b)List the angles that are less than m<5
c)List the angles that are greater than m<8
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Homework QuizHomework Quiz Write down the work and Write down the work and
answer for the following:answer for the following: 1.) pg. 349 #221.) pg. 349 #22
2.) Use the figure at the 2.) Use the figure at the right to determine which right to determine which angle has the greatest angle has the greatest measure.measure.• a) <1, <5, or <6a) <1, <5, or <6• b) <3, <11, or <12b) <3, <11, or <12