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Lesson 11 Guided Notes
Using your Algebra Skills 9
 A
division.
is an expression that compares two quantities by
 A
is a statement of equality between two
.
Lesson 11.1 Similar Polygons
 Figures that have the same shape and size are
figures.
 Figures that have the same shape but not necessarily the same size
are
figures.
 Two polygons are
polygons if and only if the
angles are
and the
sides are proportional.
 The dilation of a polygon is a non-rigid transformation by a scale
factor. The polygon retains its shape, but its size is either
increased or decreased by the scale factor.
Dilation Similarity Conjecture
 If one polygon is the image of another polygon under a dilation,
then the polygons are
.
Lesson 11.2 Similar Triangles
AA Similarity Conjecture
 If
angles of one triangle are congruent to
angles of another triangle, then the triangles are
.
SSS Similarity Conjecture
 If the
sides of one triangle are proportional to the
sides of another triangle, then the two triangles are
.
SAS Similarity Conjecture
 If
sides of one triangle are proportional to
of another triangle and the
then the two triangles are
.
sides
,
Lesson 11.4 Corresponding Parts of Similar Triangles
Proportional Parts Conjecture
 If two triangles are similar, then the corresponding
, and
are
,
.
Angle Bisector/Opposite Side Conjecture
 A bisector of an angle in a triangle divides the opposite side into
two segments whose lengths are in the same ratio as
the
of the two
forming the
.
Mini-investigation Conjectures (pg 590 and pg 591)
 The altitude to the
of a right triangle divides the
triangle into two right triangles that are
to each other
and to the original
.
 The altitude (length h) to the
of a right triangle
divides the
into two segments (lengths p and q),
such that p = ? .
?
q
Lesson 11.5 Proportions with Area and Volume
Proportional Areas Conjecture
 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
.

are solids that have the same shape but not
necessarily the same size.
 All
are similar, but not all cylinders are similar.
 Two polyhedrons are similar if all their
similar and the lengths of their
.
faces are
edges are
 Two right cylinders (or right cones) are similar if their
are
.
and
Proportional Volumes Conjectures
 If corresponding edges (or radii, or heights) of two similar solids
compare in the ratio m , then their volumes compare in the
n
ratio
.
Lesson 11.6 Proportional Segments Between Parallel Lines
Parallel/Proportionality Conjecture
 If a line parallel to one side of a triangle passes through the other
two sides, then it divides the other two sides
.
Conversely, if a line cuts two sides of a triangle
, then
it is
to the third side.
Extended Parallel/Proportionality Conjecture
 If two of more lines pass through two sides of a triangle parallel to
the third side, then they divide the two sides
.