Big Ideas Math Geometry Chapter 8 :: Postulates, Properties, & Theorems 21/22

Side-Angle-Side (SAS) 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.If ∠X ≅ ∠M and ZX/PM = XY/MN , then △XYZ ∼ △MNP

Side-Side-Side (SSS) Similarity Theorem

If the corresponding side lengths of two triangles are proportional, then the triangles are similar. If AB/RS = BC/ST , then △ABC ∼ △RST.

Angle-Angle (AA) Similarity Theorem

If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar. If ∠A ≅ ∠D and ∠B ≅ ∠E, then △ABC ∼ △DEF

Areas of Similar Polygons

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

Perimeters of Similar Polygons

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

Similar figures

Same shape but not necessarily the same size

corresponding angles

matching angles in similar shapes, which have equal measures

corresponding sides

matching sides of two similar figures

proportion

two fractions set equal to each other