Chapter 8

Question 0

Note #1

Answer 0

Ratios are always in simplest form.

Question 1

Ratio

Answer 1

Comparison of two numbers using division.

Question 2

Notes #2

Answer 2

Ratios must compare the same units

Question 3

Note #3

Answer 3

a to b doesn’t equal b to a (generally)

Question 4

Proportion

Answer 4

Equation stating that two ratios are equal.

Question 5

Cross-Product

Answer 5

If a/b=c/d, then a•d=b•c

Question 6

Reciprocal Property

Answer 6

If a/b=c/d, then b/a=d/c

Question 7

Interchange Means Property

Answer 7

If a/b=c/d, then a/c=b/d

Question 8

Geometric Means

Answer 8

The geometric mean of 2 numbers a and b is the positive number x such that a/x=x/b

Question 10

Nameless Property

Answer 10

A/b=c/d if and only if a+b/b=c+d/d

Question 11

Similar Polygons

Answer 11

Two polygons are similar if

1. ) Their corresponding angles are congruent
2. ) The lengths of corresponding sides are proportional

Question 12

Scale Factor

Answer 12

Common Ratio of 1/2 or 1:2

Question 13

Theorem 8.1

Answer 13

If two polygons are similar, then the ratio of their perimeters is equal to the ratio of their corresponding sides.

Question 14

AA Similarity Postulate

Answer 14

If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar.

Question 15

SSS Similarity Theorem

Answer 15

If corresponding sides of two of two triangles are proportional, then the two triangles are similar.

Question 16

SAS Similarity Theorem

Answer 16

If an angle of one triangle is congruent to an angle of a second triangle and the lengths of the sides including these angles are proportional, then these triangles are similar.

Question 17

Triangle Proportionality Theorem

Answer 17

If a line parallel to one side of a triangle intersects the other two sides, then it divides the 2 sides proportionally.

Question 18

Triangle Proportionality Converse

Answer 18

If a line divides 2 sides of a triangle proportionally, then it is parallel to the 3rd side.

Question 19

Theorem 8.6

Answer 19

If 3 parallel lines intersect 2 transversals, then they divide the transversals proportionally

Question 20

Theorem 8.7

Answer 20

If a ray bisects an angle of a triangle, then it divides the opposite side into segments whose lengths are proportional to the lengths of the other 2 sides.