Download Unit 4: Similarity Study Guide Simplifying ratios: be sure to convert to

Unit 4: Similarity Study Guide

Simplifying ratios: be sure to convert to the same units of measurement first

Solving proportions for a variable: cross multiply then solve for the value of the variable

Scale factor: ratio of the lengths of two corresponding sides of two similar polygons
Properties of Proportions
(1)
a c
b d
 is equivalent to  .
b d
a c

a c
a b
 is equivalent to  .
b d
c d

a c
ab c d

(3)  is equivalent to
b d
b
d


Theorem

Similar polygons
Description
Two polygons are
similar if corresponding
angles are congruent and
corresponding side
lengths are proportional
Angle-Angle
Similarity (AA ~)
If two angles of one
triangle are congruent to
two angles of another
triangle, then the two
triangles are similar.
(2)

How to Apply It
(1) Take the reciprocal of each ratio
“flip” each ratio
(2) switch the means
(3) add the denominator to the numerator
Image
K  Y and J  X
Side-Angle-Side
Similarity (SAS ~)
If two sets of
corresponding sides are
proportional and the
included angle is
congruent, then the
triangles are similar.

AB AC

and A  Q
QR QS
Side-Side-Side
Similarity (SSS ~)
If all three
corresponding sides are
proportional, then the

triangles are similar.

AB AC BC


QR QS BS
Side-Splitter
Theorem
If a line is parallel to one
side of a triangle and
intersects the other two
sides, then it divides
those sides
proportionally.
XR YS

RQ SQ
Corollary to the
Side-Splitter
Theorem
If three parallel lines
intersect two
transversals, then the
 on
segments intercepted
the transversals are
proportional.
AB WX

BC XY
Perimeters and Areas of Similar Figures


Scale factor: ratio of the lengths of two corresponding sides of two similar polygons

Ratio of Perimeters = Scale Factor

Ratio of Areas = Scale Factor 2