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similar figures

Figures that have the same shape, but not necessarily the same size.

Angle-Angle Similarity Postulate

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

Side-Side-Side Similarity Theorem

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

Side-Angle-Side 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.

Proving Similar Triangles

If an altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed are similar to the original triangle and to each other.

Areas of Similar Polygons

If two polygons are similar with the lengths of corresponding sides in the ratio of a:b, then the ratio of their areas is a ²:b ².

similar solids theorem

If two similar solids have a scale factor of a:b, then corresponding areas have a ratio of a ²:b ², and corresponding volumes have a ratio of a³:b³.

Symmetry

A plane figure that can be folded along a line so the two parts match.

line of symmetry

The line that divides two matching parts. It can be vertical, horizontal, or diagonal.

Similar shapes

Similar shapes have the same shape, but not the same size

197. 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.

198. Side-Side-Side (SSS) Similarity Theorem

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

199. 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.