Chapter 8 Test

Question 0

Proportion

Answer 0

An equation involving 2 or more ratios.

Question 1

Rules of Ratios

Answer 1

1. ALAWYS REDUCE to lowest terms
2. Convert/cancel UNIT so ratio is dimensionless
3. Fractions NEVER contain decimals OR other fractions or mixed numbers

Question 2

Means-Extremes Product Theorem

Answer 2

In a proportion, the product of the means = product of the extremes

i.e. cross multiplication

Question 3

Means-Extremes Ratio Theorem

Answer 3

Means may be interchanged and/or extremes may be interchanged (without invalidating the equality)

Question 4

Reciprocal Property of Proportions

Answer 4

If you interchange both the means AND the extremes you have this property.

Given:
a/b=c/d Ex. boys to girls

Then:
b/a=d/c Ex. girls to boys

where denominators don’t = 0

Question 5

Property of Proportions

Answer 5

An equation is still valid if the same multiple of each denominator is added to its numerator on BOTH sides.

Given:
a/b=c/d

Then:
a+nb/b=c+nd/d

where denominators don’t = 0

Question 6

Arithmetic mean

Answer 6

the average

Question 7

Geometric Mean:

Answer 7

If the means in a proportion are equal, either mean is called a geometric mean, or mean proportional, between the extremes.

1/x=x/16 and so
x^2=16
x= + or - 4

Question 8

Congruent figures

Answer 8

All corresponding angles and sides are congruent

Question 9

Similar figures

Answer 9

All corresponding angles are congruent and all ratios of corresponding sides are equal

Question 10

Scale factor

Answer 10

k, the ration which compares corresponding sides in the image to those in the original figure. It must be equal for all pairs of corresponding parts for the figures to be similar.

Question 11

Dilation

Answer 11

When a figure is enlarged

Question 12

Reduction

Answer 12

when a figure is shrunk

Question 13

Theorem 1:

Answer 13

If 2 polygons are similar, then their perimeters are in the same ratios as their sides

Question 14

AAA Postulate

Answer 14

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

Question 15

AA Theorem

Answer 15

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

Question 16

SSS Theorem

Answer 16

If the rations of the measures of three pairs of corresponding sides in two triangles are the same, then the two triangles are similar

Question 17

SAS Theorem

Answer 17

If the ratios of the measures of two pairs of corresponding sides are equal AND the included angles off each triangle are congruent, then the triangles are similar

Question 18

CASTC

Answer 18

Theorem means: If two triangles are similar, then corresponding angles are congruent.

So…

Corresponding angles of similar triangles are congruent

We can use ________ before we say this

• SAS
• SSS

Question 19

CSSTP

Answer 19

Theorem means: If 2 triangles are similar, then corresponding sides are proportional

So…

Corresponding sides of similar triangles are congruent

We can use ______ before we say this

• AA
• SAS

Question 20

Side-Splitter Theorem

Answer 20

If a line is parallel to one side off a triangle then it splits the other two sides proportionally

Question 21

Theorem 2

Answer 21

If two or more parallel lines are cut by two transversals, then the parallel lines divide the transversals proportionally

Question 22

Theorem 3

Answer 22

If a ray bisects an angles of a triangle, it divides the opposite side into segments that are proportional to the adjacent sides.