Transformations Transformation is an operation that maps the original geometric figure, the pre-image , onto a new figure called the image. A transformation can change the position, size or shape of a figure http://architecturedefined.blogspot.com/

Reflections, Translations, and Rotations

Reflection (Flip): Transformation over line called the line of reflection. Each point of the pre-image and its image are the same distance from the line of reflection Translation (slide): A Transformation that moves all points of the original figure the same distance in the same direction Rotation ( turn) : A Transformation around a fixed point called the center of rotation, through a specific angle, and a specific direction. Each point of original figure and its image are at the same distance from the center

Perpendicular Bisector theorem: If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. Converse of Perpendicular bisector theorem: If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment.

Concurrent lines: Three or more lines that intersect at a common point Concurrent lines: Three or more lines that intersect at a common point. The common point is a called point of concurrency Circumcenter Theorem: The perpendicular bisectors of a triangle intersect at a point called circumcenter that is equidistant from the vertices of the triangle Incenter Theorem: The angle bisectors of triangle intersect at a point called the incenter that is equidistant from each side of the triangle

Angle Bisector Theorem: If a point is on the bisector of an angle, then it is equidistant from the sides of the angle. Converse of the Angle Bisector Theorem: If a point in the interior of an angle is equidistant from the sides of the angle, then it is on the bisector of the angle

Medians and Altitudes of Triangles Median : It is a segment with endpoints being the vertex of the triangle and the midpoint of the opposite side Centroid: All triangles have three medians that are concurrent. Their point of concurrency is called the centroid

Centroid Theorem: The medians of a triangle intersect at a point called the centroid that is two thirds of the distance from the vertex to the midpoint of the opposite side

Altitude : A segment from the vertex to the line containing the opposite side and perpendicular to that line Orthocenter : The lines containing the altitudes of a triangle are concurrent, intersecting at point called the orthocenter