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74 Notes and answers Reg Geo.notebook
1
October 23, 2015
Oct 218:02 AM
Use properties of similar triangles to find segment lengths.Apply proportionality and triangle angle bisector theorems.
Objectives
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Artists use mathematical techniques to make twodimensional paintings appear threedimensional. The invention of perspective was based on the observation that far away objects look smaller andcloser objects look larger.
Mathematical theorems like the Triangle Proportionality Theorem are important in making perspective drawings.
74 Notes and answers Reg Geo.notebook
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Example 1: Finding the Length of a Segment
Find US.
74 Notes and answers Reg Geo.notebook
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October 23, 2015
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Check It Out! Example 1 Find PN.
Substitute in the given values.
Cross Products Prop.2PN = 15
PN = 7.5 Divide both sides by 2.
Use the Triangle Proportionality Theorem.
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74 Notes and answers Reg Geo.notebook
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Example 2: Verifying Segments are Parallel
Verify that
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Check It Out! Example 2
Since , by the Converse of the
Triangle Proportionality Theorem.
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Example 3: Art ApplicationSuppose that an artist decided to make a larger sketch of the trees. In the figure, if AB = 4.5 in., BC = 2.6 in., CD = 4.1 in., and KL = 4.9 in., find LM and MN to the nearest tenth of an inch.
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Given
Check It Out! Example 3
2.4(LM) = 1.4(2.6)
LM ≈ 1.5 cm2.4(MN) = 2.2(2.6)
MN ≈ 2.4 cm
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The previous theorems and corollary lead to the following conclusion.
74 Notes and answers Reg Geo.notebook
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Example 4: Using the Triangle Angle Bisector Theorem
Find PS and SR.
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Check It Out! Example 4
Find AC and DC.
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Oct 219:49 AM
Assignment(p. 498) 120
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