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ratio

A comparison of two quantities, also know as fancy word for fraction.

proportion

An equation that states that two ratios are equal.

Extremes

the first and last numbers in a proportion

Means

the middle two numbers in a proportion

extended ratio

compares three or more numbers

Cross Products Property

in a proportion, the product of the extremes equals the product of the means

similar figures

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

Side-Angle-Side Similarity (SAS∼)

two triangles are said to be similar when two pairs of side lengths are proportional and the included angles are congruent

geometric mean

the square root of the product of the extremes or means

Properties of Proportions

If a ÷ b = c ÷ d, then b ÷ a = d ÷ c;

scale factor

the ratio of corresponding linear measurements of two similar figures

extended proportion

when three or more ratios are equal

Angle-Angle Similarity (AA∼)

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

Side-Side-Side Similarity (SSS∼)

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

indirect measurement

methods of determining lengths that are difficult to measure

The Altitude of a Right Triangle Theorem

The altitude to the hypotenuse of a right triangle divides the triangle into two triangles that are similar to the original triangle and to each other.

Corollary 1 to the Altitude of a Right Triangle Theorem

The length of the altitude to the hypotenuse of a right triangle is the geometric mean of the lengths of the segments of the hypotenuse.

Side-Splitter Theorem

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

Corollary to the Side-Splitter Theorem

If three parallel lines intersect two transversals, then the segments intercepted on the transversals are proportional.

Triangle-Angle-Bisector Theorem

If a ray bisects an angle of a triangle, then it divides the opposite side into two segments that are proportional to the other two sides of the triangle.

Similar

figures that have the same shape but not necessarily the same size; corresponding angles are congruent, but not necessarily corresponding sides

Congruent

A plane figure with the same size and shape.

Dilation

a transformation that changes the size of an object, but not the shape

Pre-image

the original figure BEFORE a transformation is performed on it

image

the resulting figure AFTER a transformation is performed on it

enlargement

dilation whose image is larger than its preimage; |r| > 1

reduction

dilation whose image is smaller than its preimage;