T/GEOMETRY - UNIT 5

Polygons must have which of the following characteristics to be considered similar?

A 1:1 correspondence in vertices Corresponding angles are equal. Both polygons are the same shape Corresponding sides are proportional.

altitude of a triangle

An altitude of a triangle is a perpendicular line from a vertex to the opposite side.

Proportion

An equation that states that two ratios are equal

geometric mean

For any positive real numbers a, b, and x, if then x is called the geometric mean between a and b. Notice that

Ratio

The comparison of two numbers by division. The quotient is the ratio of the two numbers.

sine ratio

With respect to an acute angle of a right triangle, the ratio formed by the side opposite the acute angle over the hypotenuse.

cosine ratio

With respect to an acute angle of a right triangle, the ratio of the side adjacent to the angle over the hypotenuse

Similar polygons (shown by ~ ):

polygons whose vertices can be matched in 1:1 correspondence so that corresponding angles are equal and corresponding sides are in proportion.

Projection of a point on a line

the point where a perpendicular through the point to the line intersects the line.

Projection of a segment on a line

the portion of a line with endpoints that are the projections of the endpoints of the segment.