Triangle Congruence

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Triangle Congruence by Mind Map: Triangle Congruence

1. Congruence & Transformations

1.1. Dilation

1.1.1. A transformation in which the lines connecting every point P with its preimage 'P all intersect at a point c known as the center of the dilation

1.2. Isometry

1.2.1. A transformation that dies nit change the size or shape of a figure

1.3. rigid transformation

1.3.1. Another name for isometry

2. Classifying Triangles

2.1. acute triangle

2.1.1. A triangle that has 3 acute angles

2.2. equiangular triangle

2.2.1. A triangle with three congruent angles

2.3. right triangle

2.3.1. A triangle with one right angke

2.4. obtuse triangle

2.4.1. A triangle with one obtuse angle

2.5. equilateral triangle

2.5.1. A triangle with three congruent sides

2.6. isosceles triangle

2.6.1. A triangle with at least two congruent sides

2.7. Scalene Triangle

2.7.1. A triangle with no congruent sides

3. Angle Relationships in Triangles

3.1. auxiliary

3.1.1. A line drawn in a figure to aid in a proof

3.2. corollary

3.2.1. A theorem whose proof follows directly from another theorem

3.3. interior

3.4. exterior

3.5. interior angle

3.5.1. An angle formed by two sides of a polygon with a common vertex

3.6. exterior angle

3.6.1. An angle formed by one side of a polygon and the extension of an adjacent side

3.7. remote interior angle

3.7.1. An interior angle of a polygon that is not adjacent to the exterior angle

4. Congruent Triangles

4.1. corresponding angle

4.1.1. Angles in the same relative position in two different polygons that have the same number of angles

4.2. corresponding sides

4.2.1. Sides in the same relative position in two different polygons that have the same number of sides

4.3. congruent polygons

4.3.1. Two polygons whose corresponding sides and angles are congruent

5. Triangle Congruence:SSS and SAS

5.1. triangle rigidity

5.1.1. 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

5.2.1. The angle formed by two adjacent sides of a polygon

6. Triangle Congruence: ASA, AAS, and HL

6.1. Included side

6.1.1. The common side of two consecutive angles of a polygon.