Similarity Unit Review Flashcards
What are the 3 rules for simplifying radicals?
- No perfect square factors of the number under the radical.
- No radicals in the denominator of a fraction.
- No fractions allowed under the radical.
When there is a radical in the denominator of a fraction, how do we fix the problem?
Multiply the numerator and denominator by the radical in the denominator.
What do you do when there is a fraction under the radical?
Split the fraction in to two separate radicals and simplify if necessary.
Define ratio
A comparison of two numbers
What are the 3 forms for a ratio?
Fraction form, colon form, word form.
What is the simplified form of a ratio?
Reduced
Define proportion
Two equal ratios
What are the b and c terms in a proportion called?
The means
What are the a and d terms in a proportion called?
The extremes
What are the two methods you can use to solve a proportion?
Using a common multiple, or cross multiplication.
What are the two methods for solving geometric problems with proportional figures?
The x and y methods
How do you use the ‘x method’ to solve geometric problems with proportional figures?
Set up a proportion, then make one of the missing values ‘x’, and the other in terms of x. Then cross multiply and solve.
What is x in the ‘x method’?
One of the missing values.
How do you use the ‘y method’ to solve geometric problems with proportional figures?
Multiply each part of the given ratio by y, set up an equation (not a proportion) and solve the equation.
What is y in the ‘y method’?
The value that the original ratio was reduced by to yield the given simplified version.
Define similar polygons
Two polygons with all corresponding angles congruent (same shape) and all corresponding sides proportional (proportional sizes)
How do you show the corresponding sides of similar polygons are proportional?
Set up the ratios of the corresponding side lengths, and reduce them - showing that they all reduce to the same ratio.
The reduced ratio of corresponding sides of similar polygons is known as what?
Scale Factor
How do you find the scale factor?
Set up the ratio of any of the corresponding side lengths, and reduce it.
What is true about the perimeters of similar polygons?
They are in the same ratio as the side lengths (the same scale factor)
How do you find missing side lengths in similar polygons?
Set up a proportion using the scale factor and solve for the missing length.
What are the 3 methods of proving triangles similar?
Angle - Angle (AA), Side Angle Side (SAS), and Side Side Side (SSS)
To use SAS to prove two triangles similar, what do you have to show?
Any two sets of corresponding sides are proportional, and the corresponding included angles are congruent.
To use SSS, what do you have to show?
All three sets of corresponding sides are proportional.
In similar triangles, what things are proportional?
Corresponding sides, corresponding altitudes, corresponding medians, and the perimeters.
What is true about three or more parallel lines that intersect multiple transversals?
They divide the transversals proportionally.
What is true about a line that is parallel to one side of a triangle and intersects the other 2 sides?
It divides the other two sides proportionally.
What does the angle bisector do to the opposite side of a triangle?
It divides the opposite side proportionally to the other two sides of the triangle.
