Triangle Congruence

1. Congruence and Transformation

1.1. Dilation - stretches or shrinks the original figure

1.2. Isometry - A linear transformation which preserves length

1.3. Rigid Transformation - transformation of the plane that preserves length, reflection, translation, rotation.

2. Classifying

2.1. Acute Triangle - less than 90 degree angle

2.2. Equiangular triangle - interior angles are equal in measure

2.3. Right Triangle - an angle which is 90 degree

2.4. Obtuse triangle - more then 90 degree

2.5. Equilateral Triangle - is a triangle in which all three sides are equal.

2.6. isosceles triangle - having not just two, but all three sides and angles equal.

2.7. scalene triangle - that has three unequal sides, such as those illustrated above

3. Angle relationship in triangles

3.1. Auxiliary Line - is an extra line needed to complete a proof in plane geometry

3.2. Corollary - statement is that an equilateral triangle is also equiangular.

3.3. Interior -

3.4. Exterior

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 -

4. Congruent Triangle

4.1. Corresponding angle - the angles that occupy the same relative position at each intersection where a straight line crosses two others.

4.2. Corresponding sides - pair of matching angles or sides that are in the same spot in two different shapes.

4.3. Corresponding polygons - All the angles in a rectangle are congruent to each other and now check that the sides are proportional to each other.

5. Triangle congruence: SSS and SAS

5.1. 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

5.2. Included angle - s the angle between two sides of a triangle. It can be any angle of the triangle, depending on its purpose

6. Triangle congruence: ASA, AAS, and HL

6.1. Included sides - The common leg of two angles