20 terms

Angle-Angle Similarity Postulate (AA~ Post.)

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

Side-Side-Side Similarity Theorem (SSS~ Thm. )

If the three sides of one triangle are proportional to the three corresponding sides of another triangle, then the triangles are similar

Side-Angle-Side Similarity Theorem (SAS~ Thm. )

If two sides of one triangle are proportional to two sides of another triangle and their included angles are congruent, then the triangles are similar

Triangle Proportionality Theorem (Δ Proportionality Thm.)

If a line parallel to a side of a triangle intersects the other two sides, then it divides those sides proportionally

Converse of the Triangle Proportionality Theorem (Conv. of Δ Proportionality Thm.)

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

Two-Transversal Proportionality Corollary (2-Transv. Proportionality Cor.)

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

Triangle Angle Bisector Theorem (Δ∠ Bisector Thm.)

An angle bisector of a triangle divides the opposite side into two segments whose lengths are proportional to the lengths of the other two sides

Proportional Perimeters and Areas 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^2/b^2, or (a/b)^2.

Ratio

compares two numbers by division

Extremes

In the proportion a/b=c/d, a and d are the _

Means

In the proportion a/b=c/d, b and c are the _

Similar Polygons

Two polygons are ____________ if and only if their corresponding angles are congruent and their corresponding side lengths are proportional

Reflexive property of similarity

ΔABC~ΔABC

Symmetric Property of Similarity

If ΔABC ~ ΔDEF, then ΔDEF~ΔABC

Transitive Property of Similarity

If ΔABC~ ΔDEF and ΔDEF~ΔXYZ, then ΔABC~ΔXYZ

Indirect measurement

Any method that uses formulas, similar figures, and/or proportions to measure and object

Scale drawing

Represents an object as smaller than or larger than its actual size

Scale

Ratio of any length in drawing to the corresponding actual length

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