Triangle Similarity and Proportionality Concepts

These flashcards cover key vocabulary and concepts related to triangle similarity, congruence, and proportionality.

Similarity Statement

A statement that two geometric figures are similar, indicating that their corresponding angles are equal and their sides are proportional.

Congruent Figures

Figures that have the same shape and size, meaning all corresponding sides and angles are equal.

AA Theorem

The Angle-Angle Theorem states that if two triangles have two angles that are equal, then the triangles are similar.

SAS Similarity Postulate

If an angle of one triangle is equal to an angle of another triangle and the lengths of the sides including these angles are proportional, the triangles are similar.

SSS Similarity Postulate

If the corresponding sides of two triangles are in proportion, then the triangles are similar.

Geometric Mean

The geometric mean of two numbers is the positive square root of their product.

Side Splitter Theorem

If a line is drawn parallel to one side of a triangle, it divides the other two sides into segments of proportional lengths.

Area Ratio of Polygons

The ratio of the areas of two similar polygons is equal to the square of the ratio of their corresponding side lengths.

Proportional Sides

In similar triangles, the lengths of corresponding sides are in proportion to each other.

Counterexample

An example that disproves a statement or theorem.