Triangle Congruence
by Payge Martin
1. SSS and SAS
1.1. Triangle Rigidity: A property of triangles that states that if the side lengths of a triangle are fixed, the triangle can have only one shape.
1.2. Included Triangle: An included angle is the angle between two sides of a triangle.
2. ASA, AAS, and HL
2.1. Included side: The common leg of two angles.
3. Angle Relationships in Triangles
3.1. Auxilary Triangle: an extra line needed to complete a proof in plane geometry.
3.2. Corollary: an equilateral triangle is also equiangular.
3.3. Interior: Any of the four angles formed inside two straight lines when these lines are intersected by a third straight line.
3.4. Exterior: an angle formed outside parallel lines by a third line that intersects them
3.5. Interior Angle: the angle between adjacent sides of a rectilinear figure.
3.6. Exterior Angle: the angle between a side of a rectilinear figure and an adjacent side extended outward.
3.7. Remote Interior Angle: An exterior angle of a triangle, or any polygon, is formed by extending one of the sides of the triangle (or polygon).
4. Congruence and Transformations
4.1. Dilation: Stretches or shrinks the original figure.
4.1.1. Isometry: The plane is a linear transformation which preserves length.
4.1.1.1. Rigid Transformation: Is a transformation of the plane that preserves length.
5. Classifying Triangles
5.1. Acute Triangle: a triangle with all three angles acute (less than 90°).
5.1.1. Equiangular Triangle: a triangle where all three interior angles are equal in measure.
5.1.1.1. Right Triangle: a triangle in which one angle is a right angle (that is, a 90-degree angle).
5.1.1.1.1. Obtuse Angle: is a triangle in which one of the angles is an obtuse angle.