1. Classifying Triangles
1.1. Vocabulary
1.1.1. acute triangle - a triangle with three acute angles
1.1.2. equiangular triangle - a triangle with three congruent angles
1.1.3. right triangle - a triangle with one right angle
1.1.4. obtuse triangle - a triangle with one obtuse angle
1.1.5. equilateral triangle - three congruent sides
1.1.6. isosceles triangle - a triangle with at least two congruent sides
1.1.7. scalene triangle - a triangle with no congruent sides
1.2. You can classify triangles by sides and angles.
2. Triangle Congruence: ASA, AAS, and HL
2.1. Vocabulary
2.1.1. included side
2.2. If two angles and the included side of one triangle are congruent to the corresponding angles and included side of another triangle, they are congruent.
2.3. If two angles and a nonincluded angle of one triangle are congruent to the corresponding angles and nonincluded side of another triangle, they are congruent.
3. Angle Relationships in Triangles
3.1. Vocabulary
3.1.1. auxiliary line - a line drawn in a figure to aid in a proof
3.1.2. corollary - a theorem whose proof aids directly from another theorem
3.1.3. interior - the set of all points inside the figure
3.1.4. exterior - the set of all points outside the figure
3.1.5. interior angle - an angle formed by two sides of a polygon with a common vertex
3.1.6. exterior angle - an angle formed by one side of a polygon and the extension of an adjacent side
3.1.7. remote interior angle - an interior angle of a polygon that is not adjacent to the exterior angle
3.2. Triangulation - A method used in surveying
4. Congruent Triangles
4.1. Vocabulary
4.1.1. corresponding angles - two nonadjacent angles, one interior, one exterior, that lie on the same side of the transversal
4.1.2. corresponding sides - sides that have the same relative position in polygons
4.1.3. congruent polygons - two polygons are congruent polygons only if their corresponding angles and sides are congruent.
4.2. Corresponding angles and sides are in the same position in polygons with an equal number of sides.
5. Triangle Congruence: SSS and SAS
5.1. Vocabulary
5.1.1. included angle - an angle formed by two adjacent sides of a polygon
5.1.2. triangle rigidity - a shortcut proving if two triangles are congruent
5.2. Triangle Rigidity - If the side lengths of a triangle are given, the triangle can only have one shape. If three sides of one triangle to three sides of another triangle, they are congruent.
6. Congruence and Transformations
6.1. Vocabulary
6.1.1. Dilation - a transformation that changes the size of the figure, but not its shape
6.1.2. Isometry - a transformation that does not change the size or shape of the figure
6.1.3. Rigid Transformation - another name for isometry
6.2. Transformation - a change in the position, shape, or size of a figure
6.2.1. Translation - slides
6.2.2. Reflection - flips
6.2.3. Rotation - turns
6.2.4. Dilation