dia
Root meaning "through" or "across
di
Root meaning "two" or "twice
trans
Root meaning "across, beyond, through, so as to change
Transformation
A change in the position, shape, or size of a figure.
Types of Transformations
Translations - (slide horizontally and vertically)
Reflections - (flip across x-axis and y-axis)
Rotations - (turn about a point either CW or CCW
Clockwise or Counterclockwise)
Dialations - (scaling, increase or decreace by a scale factor
Dialation
Enlarging or reducing a figures proportionally.
iso
Root meaning "equal" or "homogeneous: uniform
Isometry
A transformation whose length, angle measures, and area are the same when mapped onto its original space or a second space.
Rigid Transformation
Another name for Isometry, it is a transformation that does not change the size or shape of a figure
Triangle
3-sided polygon whose angle measures add up to equal 180�. Triangles are classified by angle or side measures and there are seven classifications. Acute, Equalangular, Right, Obtuse, Equalateral, Isosceles, and Scalene
Triangle Sum Theorem
The sum of the angle measures of any triangle equals 180�.
Acute Triangle
A triangle whose interior angles are all "acute" or less than 90�. Has 3 Acute angles.
Equalangular Triangle
A triangle with all congruent angles each equaling 60�. Has 3 equal 60� angles.
Right Triangle
A triangle that has one 90� angle. Has 1 right angle.
Obtuse Triangle
A triangle where one angle measures obtuse (> 90�). Has 1 obtuse angle.
Equalateral Triangle
A triangle with three congruent sides (all equal length). Has 3 sides with the same length).
Isosceles Triangle
A triangle with two congruent sides (equal in length). Has at least 2 equal side lengths.
Scalene Triangle
A triangle that has no equal sides. All 3 sides are different lengths. No congruent sides.
Auxillary Line
A line added to a figure to help in a proof.
Corallary
A theorem whose proof follows directly from another theorem.
Acute Angles Corollary
The acute angles (those less than 90�) of a right triangle are complementary (which means they add to equal 90�).
Equalangular Triangle Corollary
The angle measures are all congruent and equal to 60� each.
Interior
Inner or internal part. Set of all points inside a figure.
Exterior
Outside or exterior part. Set of all points outside a figure.
Interior Angle
An angle inside a shape. An interior angle is formed by two sides of a triangle.
When you add up the Interior Angle and Exterior Angles you get a straight line, 180�.
Exterior Angle
An angle formed by one side of a triangle and the extension of an adjacent side. Each exterior angle has two remote interior angles.
Remote Interior Angle
An interior angle that is not adjacent to the exterior angle. (These are two nonadjacent interior angles corresponding to each exterior angle of a triangle).
Exterior Angle Theorem
The measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles.
Third Angles Theorem
If two angles of one triangle are congruent to two angles of another triangle, then the third pair of angles are congruent.
Corresponding Angles
Angles in the same place on different figures.
Corresponding Lines
Lines (or sides) in the same place or different figures.
Congruent Polygons
Polygons with same size and shape. For examplg e triangles that are the same sixe and shape are congruent since their corresponding angles and sides are congruent.
Triangle Rigidity
A shortcut for proving two triangles are congruent. SSS congruence, SAS congruence, etc.
SSS (Side-Side-Side) Congruence
If three sides of one triangle are congruent to three side of another triangle, then the triangles are congruent.
SAS (Side-Angle-Side) Congruence
If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.
Included Angle
The angle formed by two adjacent sides.
Included Side
The common side between two consecutive angles.
ASA (Angle-Side-Angle) Congruence
If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.
AAS (Angle-Angle-Side) Congruence
If two angles and a non-included side of one triangle are congruent to the corresponding angles and non-included side of another triangle, then the triangles are congruent.
CPCTC (Corresponding Parts of Congruent Triangles are Congruent)
Used as a justification in a proof after you have proven two triangles congruent.
Coordinate Proof
A type of proof where a figure is drawn on a coordinate plane and formulas are used to prove properties of figures.
Legs of an Isosceles
The two congruent sides of an isosceles triangle.
Vertex Angle
The angle formed by the legs of an isosceles triangle (opposite the base).
Base of Isosceles Triangle
The side opposite the vertex angle.
Base Angles
The side opposite the vertex angle is called the base. The angles of an isosceles triangle that have a base as a side.
Isosceles Triangle Theorem
If two sides of a triangle are congruent, then the angles opposite the sides are congruent.
Converse of Isosceles Triangle Theorem
If two angles of a triangle are congruent, then the side opposite those angles are congruent.