ASN PRACTICE

Question 1

ratio

Answer 1

quotient of two numbers

Question 1

proportion

Answer 1

equation stating that two or more ratios are equal.

Question 2

THEOREM 59:in a proportion, the product of the ________ is euqivalent to the product of the ________

Answer 2

means, extremes (means-extremes product theorem, allows you to cross multiply)

Question 2

THEOREM 60: if the product of a pair of nonzero numbers is equal to the product of another pair of nonzero numbers, then either pair of numbers may be made the extremes, and the other pair the means, of a proportion

Answer 2

(means-extremes ratio theorem)
example: given that pq=rs, we can created proportions such as p/r=s/q, p/s=r/q, r/p=q/s. all of these proportions are equivalent forms, since multiplying them out yields equivalent equations

Question 3

in a mean proportion…

Answer 3

…the means are the same
ex: 1/4=4/16 (numerator and denominator are the same (4))

Question 4

if the means of a proportion are equal…

Answer 4

…either mean is called a geometric mean, or mean proportional, between the extremes

Question 5

similar polygons are polygons in which:

Answer 5

1. the ratios of the measures of corresponding sides are equal
2. corresponding angles are congruent

Question 6

ways you can prove that triangles are similar

Answer 6

1. AAA (measure of corresponding angles ~)
2. AA (measure of two corresponding angles ~)
3. SSS~ (ratio of measure of three corresponding sides ~)
4. SAS~ (ratios of the measure of two corresponding sides are equal + included angle congruent)

Question 6

theorem 61: the ratio of the two _____________ equals the ratio of any pair of __________________

Answer 6

similar polygons, corresponding sides

Question 7

once we know two triangles are similar, we can use the definition of similar polygons to prove that

Answer 7

1. corresponding sides of the triangles are proportional (the ratio of the measures of corresponding sides are equal)
2. corresponding angles of the triangles are congruent

Question 8

INDICATE IF A-S-N: if two triangles are similar, then they are congruent

Question 8

INDICATE IF A-S-N: if two triangles are congruent, then they are similar

Question 8

INDICATE IF A-S-N: an obtuse triangle is similar to an acute triangle

Question 8

INDICATE IF A-S-N:

Question 9

INDICATE IF A-S-N:

Question 10

INDICATE IF A-S-N:

Question 10

INDICATE IF A-S-N: