Post on 26-Mar-2015
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Objectives
• Apply similarity relationships in right triangles to solve for missing lengths
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Right Triangle Similarity Theorem
• The altitude to the hypotenuse of a right triangle divides the triangle into two triangles that are similar to the original triangle and to each other
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Solving Problems with Similar Right Triangles (1)
Suppose one of the above letters is an unknown.
• Step 1: Redraw the original triangle into 3 separate triangles and label the triangles with given information
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Solving Problems with Similar Right Triangles (2)
• Step 2: Set up a table with known valuesSmall leg Medium
legHypotenu
se
∆1 a b c
∆2 r h a
∆3 h s b• Step 3: Since all three triangles are similar, set up
a proportion and solve for a missing length.
Example: s
b
h
a
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Similar Right Triangles Example (1)
Step 3: Set up a proportion and solve for y.
Small leg
Medium leg
Hypotenuse
∆1 x 9
∆2 4 y x
∆3 y 5
x2 = 36
x = 6
x
x 9
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Step 3: Set up a proportion and solve for x.
5
4 y
y
y2 = 20 = 4*5
y = 52
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Similar Right Triangles Example (2)
Solve for x and y.
Step1: Redraw into 3 separate triangles; label.
Step2: Fill in the table with known information
Small leg
Medium leg
Hypotenuse
∆1 x 9
∆2 4 y x
∆3 y 5