Similarity Unit Review

Question 1

What are the 3 rules for simplifying radicals?

Answer 1

1. No perfect square factors of the number under the radical.
2. No radicals in the denominator of a fraction.
3. No fractions allowed under the radical.

Question 2

When there is a radical in the denominator of a fraction, how do we fix the problem?

Answer 2

Multiply the numerator and denominator by the radical in the denominator.

Question 3

What do you do when there is a fraction under the radical?

Answer 3

Split the fraction in to two separate radicals and simplify if necessary.

Question 4

Define ratio

Answer 4

A comparison of two numbers

Question 5

What are the 3 forms for a ratio?

Answer 5

Fraction form, colon form, word form.

Question 6

What is the simplified form of a ratio?

Answer 6

Reduced

Question 7

Define proportion

Answer 7

Two equal ratios

Question 8

What are the b and c terms in a proportion called?

Answer 8

The means

Question 9

What are the a and d terms in a proportion called?

Answer 9

The extremes

Question 10

What are the two methods you can use to solve a proportion?

Answer 10

Using a common multiple, or cross multiplication.

Question 11

What are the two methods for solving geometric problems with proportional figures?

Answer 11

The x and y methods

Question 12

How do you use the ‘x method’ to solve geometric problems with proportional figures?

Answer 12

Set up a proportion, then make one of the missing values ‘x’, and the other in terms of x. Then cross multiply and solve.

Question 13

What is x in the ‘x method’?

Answer 13

One of the missing values.

Question 14

How do you use the ‘y method’ to solve geometric problems with proportional figures?

Answer 14

Multiply each part of the given ratio by y, set up an equation (not a proportion) and solve the equation.

Question 15

What is y in the ‘y method’?

Answer 15

The value that the original ratio was reduced by to yield the given simplified version.

Question 16

Define similar polygons

Answer 16

Two polygons with all corresponding angles congruent (same shape) and all corresponding sides proportional (proportional sizes)

Question 17

How do you show the corresponding sides of similar polygons are proportional?

Answer 17

Set up the ratios of the corresponding side lengths, and reduce them - showing that they all reduce to the same ratio.

Question 18

The reduced ratio of corresponding sides of similar polygons is known as what?

Answer 18

Scale Factor

Question 19

How do you find the scale factor?

Answer 19

Set up the ratio of any of the corresponding side lengths, and reduce it.

Question 20

What is true about the perimeters of similar polygons?

Answer 20

They are in the same ratio as the side lengths (the same scale factor)

Question 21

How do you find missing side lengths in similar polygons?

Answer 21

Set up a proportion using the scale factor and solve for the missing length.

Question 22

What are the 3 methods of proving triangles similar?

Answer 22

Angle - Angle (AA), Side Angle Side (SAS), and Side Side Side (SSS)

Question 23

To use SAS to prove two triangles similar, what do you have to show?

Answer 23

Any two sets of corresponding sides are proportional, and the corresponding included angles are congruent.

Question 24

To use SSS, what do you have to show?

Answer 24

All three sets of corresponding sides are proportional.

Question 25

In similar triangles, what things are proportional?

Answer 25

Corresponding sides, corresponding altitudes, corresponding medians, and the perimeters.

Question 26

What is true about three or more parallel lines that intersect multiple transversals?

Answer 26

They divide the transversals proportionally.

Question 27

What is true about a line that is parallel to one side of a triangle and intersects the other 2 sides?

Answer 27

It divides the other two sides proportionally.

Question 28

What does the angle bisector do to the opposite side of a triangle?

Answer 28

It divides the opposite side proportionally to the other two sides of the triangle.