Geometry Unit 6 Vocabulary
Similarity Transformations
Area of a figure - Area is a measure of how much space there is on a flat surface. Area is measured in square
units.
Center of dilation – The center of dilation is a fixed point in the plane about which all points are expanded or
contracted. It is the only invariant point under a dilation.
Dilation – equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of
sides.
Distance between two points – the length of the line segment joining two points; a unique non-negative real
number.
Geometric Mean –a kind of average of a set of numbers that is different from the arithmetic average. The
geometric mean of two positive numbers a and b is the positive number x such that
a x
 . When solving,
x b
x  a  b The geometric mean of 6 and 24 is 12. The geometric mean is also called the mean proportion.
Mean Proportion - a kind of average of a set of numbers that is different from the arithmetic average. The mean
proportion of two positive numbers a and b is the positive number x such that
a x
 . When solving,
x b
x  a  b The mean proportion of 6 and 24 is 12. The mean proportion is also called the geometric mean.
Mid-segment of a triangle - A line segment joining the midpoints of two sides of a triangle.
Properties:



The mid-segment is always parallel to the third side of the triangle.
The mid-segment is always half the length of the third side.
The mid-segment is always half the length of the third side.
Perimeter – the distance around a two-dimensional shape.
.
Proportion – a statement in which two ratios are equal. It can be written in two ways:

Two equal fractions
a c

b d
Or

Using a colon
a:b  c:d
When two ratios are equal, then the product of the means equals the product of the extremes. That is, for the
proportion
a : b  c : d , ad  bc
Ratio – a comparison between two quantities
These two triangles are similar. We can prove they are similar using the ratios of their corresponding sides.



The ratio of the bottom sides is 20/15, which simplifies to 4/3.
The ratio of the right sides is 8/6, which simplifies to 4/3.
The ratio of the left sides is 16/12, which simplifies to 4/3.
Since all three ratios are equivalent, then the two triangles are similar.
Scale Factor – The ratio of any two corresponding lengths in two similar geometric figures.
Similar figures – figures whose corresponding sides have lengths that are proportional and whose
corresponding angles are congruent.
Theorems
Theorems
AA Similarity Theorem – If two angles of one triangle are congruent to two angles of another triangle, then the
triangles are similar.
Altitude Mean Theorem - The altitude to the hypotenuse of a right triangle is the geometric mean between the
segments of the hypotenuse.
Leg Mean Theorem - Each leg of a right triangle is the mean proportional between the hypotenuse and the
segment it touches on the hypotenuse.
SAS Similarity Theorem - If an angle of one triangle is congruent to an angle of another triangle and the sides
including those angles are in proportions, then the triangles are similar
SSS Similarity Theorem - If the sides of two triangles are in proportion, then the triangles are similar.
Three Similar Triangles Theorem - The altitude to the hypotenuse of a right triangle forms two triangles that are
similar to each other and to the original triangle.
Triangle Mid-segment Theorem - In any triangle, a segment joining the midpoints of any two sides will be
parallel to the third side and half its length.
Triangle Proportionality Theorem - If a line parallel to one side of a triangle intersects the other two sides, then it
divides those sides proportionally.