Chapter 6 geometry test (6.2 nor 6.6 included)

what is the ratio of one number called?

Quotient (first divided by second)

proportion

an equation stating that two ratios are equal

what is a/b = c/d equivalent to? (Properties of proportions)

ad = cb or a/c = b/d or b/a = d/c or a+b/b = c+d/d

a way to use Properties of proportions

when you have two different variables and you need to know their ratios EX: 35x = 7y to x/y = 35/7

similar polygons

same shape but necessarily the same size

when talking about two polygons what do these mean = \~ ≅

same size, shape, and size and shape

scale factor

the ratio of the lengths of 2 corresponding sides in \~ polygons

perimeters of similar polygons

if two polygons are \~ then the ratio of their perimeters is = to the ratio of their corresponding side lengths (scale factor)

Angle angle \~ postulate

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

side angle side (SAS) \~ thm

if an angle of one triangle is congruent to an angle of another triangle and the sides including those angles are in proportion the the triangles are similar

side side side (SSS) \~ thm

if the sides of two triangles are in proportion(same ratio), then the triangles are \~

the order of a scale factor in a proportion

the smallest side of one triangle goes over the smallest side of the other triangle, same with middle sides and largest sides

Triangle proportionality thm

If a line parallel to one side of a triangle intersects the other two sides then it divides the two sides proportionally (They have the same ratio)

Triangle proportionality thm converse

If a line divides two sides of a triangle proportionally then it is parallel to the third side

Thm 6.6

If three parallel lines intersect two transversals,then they divide the tranversals proportionally

Triangle Angle-Bisector thm

If a ray bisects an angle of a triangle (forms an angle bisector) then it divides the opposite sides into segment whose lengths are proportional to the other two sides. (its the ratio of the two segments on one side of the angle bisector that is proportional to each other)

note

when proving triangles \~ you can put which ever side on top when making the scale factor as long as the problem doesn’t specify by saying the order in the problem.

note

when square rooting the variable will equal the number and negative number you get

note

try to not make mixed numbers Ex 1 1/3 rather 4/3

note

remember to LABEL and simplify