Download Chapter 8 Notes

Chapter 8 Notes
Section 8.1
• Ratio: the ratio of a to b is a/b or a:b.
• Proportion: an equation that equates two ratios. Ratio a/b equals ratio c/d can be
written a/b = c/d, where a and d are the extremes and b and c are the means.
• Cross Product Property: The product of the extremes is equal to the product of the
means. If a/b = c/d, then ad = bc.
• Reciprocal Property: If two ratios are equal, then their reciprocals are also equal. If
a/b = c/d, then b/a = d/c.
Section 8.2
• Properties of Proportions:
a c
a b
 , then  .
b d
c d
a c
ab cd
If  , then

.
b d
b
d
If
• Geometric Mean: the geometric mean of two numbers a and b is the positive number
x such that a/x = x/b. If you solve for x, x equals the square root of ab, which is a
positive number.
Section 8.3
• Similar Polygons: two polygons whose corresponding angles are congruent and the
lengths of the corresponding sides are proportional.
• Theorem 8.1: If two polygons are similar, then the ratio of their perimeters (scale
factor) is equal to the ratios of their corresponding sides.
Scale Factor: The ratio of the lengths of two corresponding sides of two similar
polygons is called the scale factor.
Section 8.4
• Angle-Angle (AA) Similarity Postulate: If two angles of one triangle are congruent
to two angles of another triangle, then the two triangles are similar.
Section 8.5
• Side-Side-Side (SSS) Similarity Theorem: If the corresponding sides of two
triangles are proportional, then the triangles are similar.
• Side-Angle-Side (SAS) Similarity Theorem: If an angle of one triangle is congruent
to an angle of a second triangle and the lengths of the sides including these angles are
proportional, then the triangles are similar.
Section 8.6
• Triangle Proportionality Theorem: If a line parallel to one side of a triangle
intersects the other two sides, then it divides the two sides proportionally.
• Triangle Proportionality Theorem Converse: If a line divides two sides of a triangle
proportionally, then it is parallel to the third side.
• Theorem 8.6: If three parallel lines intersect two transversals, then they divide the
transversals proportionally.
• Theorem 8.7: If a ray bisects an angle of a triangle, then it divides the opposite side
into segments whose length are proportional to the lengths of the other two sides.
Section 8.7
• Dilation: a nonrigid transformation. A dilation with center C and scale factor k, maps
every point in plane P to a point in plane P`. A dilation is a reduction if 0 < k < 1, and
is an enlargement if k > 1.