unit 7: similarities

Question 1

ratio

Answer 1

compares 2+ quantities, with the denominator being >0

Question 2

proportion

Answer 2

an equation stating that 2 ratios are equivalent (“x is to y as a is to b” –> x/y = a/b)

Question 3

extended proportion

Answer 3

when there are 3+ equivalent ratios

Question 4

terms

Answer 4

objects of a proportion

Question 5

means-extremes property of proportions

Answer 5

aka the “cross-product property”

if a/b=c/d, then ad=bc

Question 6

properties of proportions

a/b=c/d

Answer 6

1. ad=bc (cross multiply)
2. a/c=b/d (divide cross-multiply 1&3)
3. b/a=d/c (divide cross-multiply 4&3)
4. (a+b)/d=(c+d)/d (1&2/4=3&4/4)
5. a/b=c/d=e/f, then a+c+e/b+d+f=a/b

Question 7

similarity

Answer 7

2 polygons are similar if when their vertices are paired,
1. their corresponding angles are congruent
2. their corresponding sides are proportional

Question 8

angle angle similarity postulate

Answer 8

if 2 angles of 1 triangle are congruent to 2 angles of another triangle, then the 2 triangles are similar

Question 9

triangle SAS similarity theorem

Answer 9

if an angle of 1 triangle is congruent to another triangle’s angle and the including sides of those angles are in proportion, then the triangle is similar

Question 10

triangle SSS similarity theorem

Answer 10

if the sides of 2 triangles are proportional, then the 2 triangles are similar

Question 11

CPSTP

Answer 11

Corresponding Parts of Similar Triangles are Proportional

Question 12

triangle proportionality theorem

Answer 12

if a line is parallel to 1 side of a triangle and interests the 2 other sides, then it divides those sides proportionally

Question 13

side splitter theorem

Answer 13

if 3 parallel lines intersect 2 transversals, then the segments intercepted on the transversals are proportional

Question 14

triangle angle bisector theorem

Answer 14

if 2 rays bisect a triangle, then they’re dividing the opposite side into proportional segments to the 2 other sides