unit 4 geometry vocab

similar polygons

Polygons that have the same shape but not always the same size; their angles are equal, and their sides are in proportion.

scale factor

The ratio of the lengths of two corresponding sides of similar figures.

Angle-Angle Similarity (AA~)

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

Side-Side-Side Similarity (SSS~)

If all three pairs of sides of two triangles are in proportion, the triangles are similar.

Side-Angle-Side Similarity (SAS~)

If two sides are in proportion and the included angle is equal, the triangles are similar.

gemoetric mean

The number that is between two values in proportion

altitude

a line segment drawn from a vertex of a polygon that is perpendicular to the opposite side or the line containing the oposite side

Altitude-Hypotenuse Theorem

In a right triangle, the altitude to the hypotenuse forms two smaller triangles that are similar to each other and to the original triangle.

Altitude Rule

In a right triangle, the altitude to the hypotenuse is the geometric mean between the two segments of the hypotenuse.

Leg Rule

In a right triangle, each leg is the geometric mean between the hypotenuse and the segment of the hypotenuse next to that leg.

Triangle Proportionality Theorem

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

Midsegment Theorem

A segment connecting the midpoints of two sides of a triangle is parallel to the third side and half as long.

Proportional Parts with Parallel Lines (2 ideas)

Parallel lines cut transversals into proportional segments

Proportional Parts with Parallel Lines (2 ideas)

if transversals are cut proportionally, the lines are parallel.

Special Segments of Similar Triangles

In similar triangles, corresponding altitudes, medians, and angle bisectors are in the same ratio as the sides.

Triangle Angle Bisector Theorem

The angle bisector in a triangle divides the opposite side into two segments that are proportional to the other two sides.

median

A segment from a vertex of a triangle to the midpoint of the opposite side.