7.1 Cross Product Property: If a:b =c:d and b does not = 0 and d does not = 0, then ad = bc. Example:
Properties of Proportions: a:b = c:d <--> a:c = b:d <--> b:a = d:c <--> ad = bc Example:
Partner Assignment:
7.2 Similar Polygons: Two polygons are similar polygons iff their corresponding angles are congruent and their corresponding side lengths are proportional. Similarity Ratio: The ratio of the lengths of the corresponding sides of two similar polygons.
Apartment Assignment: Total Area: about 3,797 sq. ft.
7.3 AA Similarity: If two angles on one triangle are = to two angles of another triangle, then the triangles are similar. Example: Explain why the triangles are similar and write a similarity statement.
SAS Similarity: If two sides of one triangle are proportionate to two sides of another triangle and their included angle are equal, then the triangles are similar. Example: Verify that the given triangles are similar.
SSS Similarity: If the three sides of one triangle are proportionate to the three corresponding sides of another triangle, then the triangles are similar. Example: Verify that the triangles are similar.
7.4 Triangle Proportionality Theorem: If a line parallel to a side of a triangle intersects the other two sides, then it divides those sides proportionally.
Example:AC = 36cm, and BC = 27cm. Verify that DE is parallel to AB.
Transversal Proportionality Theorem: If three or more parallel lines intersect two transversals, then they divide the transversals proportionally.
Example: In the figure, BC is parallel to DE, which is parallel to FG. Complete each proportion.
Angle Bisector Proportionality Theorem: An angle bisector of a triangle divides the opposite sides into two segments whose lengths are proportional to the lengths of the other two sides.
Example: Find AC and DC.
7.5 Proportional Perimeter and Area Theorem: If the similarity ratio of two similar figures is a:b, then the ratio of their perimeters is a:b, and the ratio of their areas is (a:b) squared. Example:
7.6 Dilation: A transformation that changes the size of a figure, but not its shape. Scale Factor: Describes how much the figure is enlarged or reduced. Example: