Chapter 7

Theorem 7.1 Perimeters of Similar Polygons

If two polygons are similar, then the ratio of their perimeters is equal to the ratios of their corresponding side lengths

Theorem 7.2 Areas of Similar Polygons

If two polygons are similar, then the ratio of their areas is equal to the squares of their corresponding side

Angle-Angle Similarity Theorem

If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are dimilar

Theorem 7.4 Side-Side-Side Similarity Theorem

If the corresponding side lengths of two triangles are proportional, then the triangles are similar

Theorem 7.5 Side-Angle-Side Similarity Theorem

If and angle of one triangle is congruent to and angle of a second triangle and the length of the sides including these angles are proportional, then the triangles are similar.

Theorem 7.6 Triangle Property Theorem

If a line to one side intersects the other two sides, then it divides the two sides proportionally

Theorem 7.7 Converse of the Triangle Proportionality Theorem

If a line divides two sides of a triangle proportionally, then it is parallel to the third side

Theorem 7.8 Three Parallel Lines Theorem

If three parallel lines intersect two transversals, then they divide the transversals proportionally

Theorem 7.9 Triangle Bisector Theorem

If a bray bisects an angle of a triangle, then it divides the oposite sides into segments whose lengths are proportional to the lengths of the two other sides