1. 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

2. Reflections, Translations, and Rotations

3. 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

4. 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.

5. 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

6. 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

7. 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

8. 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

9. 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