Transcript section 8.1-8.3 - Fulton County Schools

Daniel Cohen & Jacob Singer
8.1 = Dilations and Scale Factors
8.2 = Similar Polygons
8.3 = Triangle Similarity
Dilations and Scale Factors
Dilation = A transformation that is not rigid. Preserves the shape of an object,
but the size may vary. (Example: Your eyes will dilate to adjust to brightness).
Dilations can be found on a coordinate plane by multiplying the x and y
coordinates of a point by the same number n. D(x, y) = (nx, ny)
The number n called a scale factor.
Types of Dilations: Contraction = The sixe of a figure is reduced by the
dilation. ( l n l < 1 )
Expansion = The size of the figure is enlarged by the dilation. ( l n l > 1 )
Similar Polygons
Similar Figures = Two figures are similar if and only if one is congruent to
the image of the other by a dilation.
Proportional = When the ratios of corresponding sides of two polygons
are equal
Proportion = The statement of the equality of two ratios.
Polygon Similarity Postulate = Two polygons can only be similar if each
pair of corresponding angles are congruent, and each pair of
corresponding sides are proportional. (Hint – The letters of the vertices
of the polygons must be written in corresponding order.)
When working with similar figures, it is often helpful to know the
following:
Properties of Proportions:
Cross-Multiplication: If a / b = c / d, then ad = bc (d ≠ 0)
Reciprocal: If a / b = c / d, then b / a = d / c (a, b, c, and d ≠ 0)
Exchange: If a / b = c / d, then a / c = b / d (a, b, c, and d ≠ 0)
“Add One”: If a / b = c / d, then (a + b) / b = (c + d) / d (b and d ≠ 0)
Triangle Similarity
Here are some helpful shortcuts for determining triangle similarity! Yayyyy!
AA (Angle – Angle) Similarity Postulate: If two angles of a triangle are
congruent to two angles of another triangle, then the triangles are similar.
SSS (Side – Side – Side) Similarity Theorem: If three sides of one triangle
are proportional to the three sides of another triangle, then the triangles
are similar.
SAS (Side – Angle – Side) Similarity Theorem: If two sides of one triangle
are proportional to two sides of another triangle and their included angles
are congruent, then the triangles are similar.
Click Here to go to Polygon Similarity
land!
Click Here for fun proportion
information!
Dilations and Scale Factors Quiz
Polygon Similarity Quiz
Click Here to go to Fun Triangle Similarity
World!