Geometry- Similar Triangles

Similar polygons

Two polygons are similar iff their corresponding sides are proportional and their corresponding angles are congruent

Scale factor

If 2 shapes are similar, the ratio of sides in lowest terms

AA (Angle Angle)

Given 2 triangles if 2 pairs of angles are congruent, then triangles are similar

SSS (Side Side Side)

Given 2 triangles if all 3 pairs of corresponding sides are proportional, then triangles are similar

SAS (Side Angle Side

Given 2 triangles if 2 pairs of corresponding sides are proportional and the included angles are congruent, then the triangles are similar

Triangle Proportionality Theorum

If a line parallel to one side of a triangle intersects the other 2 sides, then it divides the 2 sides proportionally

Converse of Triangle Proportionality

If a line divides 2 sides of a triangle proportionally, then it is parallel to the 3rd side

Three parallels

If 3 parallel lines intersect 2 transversals, then they divide the transversals proportionally

Midsegment

A segment with endpoints at the midpoints of 2 sides

Midsegment theorum

The segment connecting the midpoints of 2 sides of a triangle is parallel to the third side and half as long as that side

Perpendicular bisector

A line/segment/ray through the midpoint of a side is perpendicular to the side

Perpendicular bisector theorum

If a point lies on the perpendicular bisector of a segment, then its equidistant from the endpoints of a segment

Converse of perpendicular bisector thm

If a point is equidistant from the endpoints of a segment, then it lies on the perpendicular bisector

Circumcenter

Point where all 3 perpendicular bisectors meet

Angle bisector

Segment that creates 2 conguruent angles

Angle Bisector theorem

If a point is on the bisector of an angle, then it is equidistant from the 2 sides of the angle

Converse of Angle Bisector thm

If a point is equidistant from the 2 sides of the angle, then it is on the bisector of the angle

Incenter

The point where all 3 angle bisectors meet

Median

Segment from a vertex to the midpoint of the opposite side of a triangle

Centrioid

The point where all 3 medians meet and divides median into sections: 1/3 and 2/3 of the length

Altitude

A segment from a vertex that is perpendicular to the opposite side