Transcript Ratios, Proportions, and Similar Triangles

Ratios, Proportions, and
Similar Triangles
Ratios
• Ratios are like fractions
• The ratio 1:4 means 1 part to 4 parts
and is equivalent to the fraction
1 (part:part)
4
OR
1
5
(part:whole, because there are 5 parts
altogether)
Ratio Word Problems
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3.
Attach an X to each part of the ratio
Write and solve an equation using the expressions
The ratio of two complementary angles is 1 : 2. Find
the angles.
<1 = 1x, <2 = 2x
1x + 2x = 90
3x = 90; x = 30
<1 = 30, <2 = 60
4.
5.
The ratio of two supplementary angles is 4 : 1. Find
the angles.
The ratio of the angles of a triangle is 2 : 3 : 7. Find
the angles.
A. Solving Proportions
• Cross multiply and set the products equal to each other
• Be sure to use FOIL when multiplying polynomials
• Solve for the variable
B. Properties of proportions
Similar Polygons
shape
size
Example of similar triangles
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congruent
Their corresponding angles are _______________.
direct ratio
Their corresponding sides are in a ___________________.
scale factor
2:1
This ratio is called a _______________
and in this case is ____.
We show that they are similar with this statement: ____________.