Download Geometry Unit 7 - Georgetown ISD

Word or Conjecture
Ratio
Proportion
Statement
an expression that compares two quantities by
division.
Diagram
A ratio may be written as:
two equal ratios
A proportion may be written as:
a
or a to b or a : b
b
a
b
Similar Polygons
Dilation Similarity
c
d
Two polygons are similar if and only if
1. the corresponding angles are congruent
and
2. the corresponding sides are in
proportion.
If one polygon is the image of another polygon
under a dilation, then the polygons are similar.
AA Similarity
If two angles of one triangle are congruent to
two angles of another triangle, then the
triangles are similar
SSS Similarity
If the three sides of one triangle are
proportional to three sides of another triangle,
then the two triangles are similar.
SAS Similarity
If two sides of one triangle are proportional to
two sides of another triangle and the included
angles are congruent, then the triangles are
similar.
If two triangles are similar, then the
corresponding altitudes, medians, and angle
bisectors are proportional to the corresponding
sides.
Proportional Parts

Unit 11 Vocabulary and Conjectures
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Word or Conjecture
Angle Bisector/Opposite Side
Parallel/Proportionality
Extended Parallel/Proportionality
Proportional Areas
Statement
A bisector of an angle in a triangle divides the
opposite side into two segments whose lengths
are in the same ratio as the length of the two
sides forming the angle.
If a line is parallel to one side of a triangle and
passes through the other two sides, then it
divides the other two sides proportionally.
Diagram
Conversely, if a line cuts two sides of a triangle
proportionally, then it is parallel to the third
side.
It two or more lines pass through two sides of a
triangle parallel to the third side, then they
divide the two sides proportionally.
If corresponding sides of two similar polygons
or the radii of two circles compare in the ratio
m
, then their areas compare in the ratio
n
m2
n2
Proportional Volumes
or
m
 
n
2
If corresponding edges (or radii, or heights) of
two similar solids compare in the ratio
m
,
n
then their volumes compare in the ratio
m3
n3
or
m
 
n
3
Unit 11 Vocabulary and Conjectures
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