Triangle Congruence
by Sarajah Moody
1. Angle Relationships in Triangle
1.1. Auxiliary Line-is an extra line needed to complete a proof in plane geometry.
1.1.1. Exterior Angle-the angle between a side of a rectilinear figure and an adjacent side extended outward.
1.2. Corollary-the angles opposite two congruent sides of a triangle are also congruent
1.2.1. Interior Angle- the angle between adjacent sides of a rectilinear figure.
1.3. Interior- is the set of all points inside the figure
1.3.1. Exterior- is the set of all points outside the figure
1.3.2. Remote Interior Angle- is the interior angle that is not adjacent to the exterior angle
2. Congruent Triangles
2.1. Corresponding Angles-the angles that occupy the same relative position at each intersection where a straight line crosses two others.
2.2. Cooresponding Sides- a pair of matching angles or sides that are in the same spot in two different shapes.
2.2.1. Congruent Polygons-have the same number of sides, and all corresponding sides and interior angles are congruent.
3. Triangle Congruence-SSS and SAS
3.1. 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
3.2. Included Angle-is the angle between two sides of a triangle. It can be any angle of the triangle, depending on its purpose. The included angle is used in proofs of geometric theorems dealing with congruent triangles.
4. Congruence and Transformation
4.1. Dilation- is a type of transformation that changes the size of the image.
4.2. Isometry- is a transformation that preserves length, angle measure, and area
4.3. Rigid Transformation- is another mane for isometry
5. Classifying Triangles
5.1. Acute Triangle-is a triangle with all three angles less than 90°
5.2. Equiangular Triangle- is a triangle where all three interior angles are equal in measure. Because the interior angles of any triangle always add up to 180°, each angle is always 60°
5.3. Right Triangle- is a triangle in which one angle that is, a 90-degree angle. The relation between the sides and angles of a right triangle is the basis for trigonometry
5.3.1. Obtuse Triangle-is a triangle in which one of the angles is an obtuse angle.
5.3.2. Equilateral Triangle-is a triangle in which all three sides are equal.
5.4. Isosceles Triangle- is a triangle with at least two equal sides.
5.4.1. Scalene Triangle-is a triangle that has three unequal sides