Triangle Congruency

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Triangle Congruency by Mind Map: Triangle Congruency

1. Guidelines

1.1. Anything goes!

1.2. No criticism or flaming allowed

1.3. The Wilder The Better

1.4. Quantity is Quality

1.5. Set a Time Limit

2. 4.1 Congruence & Transformations

2.1. Congruence transformations are also called isometries. Two figures that can be transformed into each other by a congruence transformation are said to be congruent.

2.2. Dilation-Extends out from the center, at the same points in all directions.

2.3. Isometry-of, relating to, or denoting muscular action in which tension is developed without contraction of the muscle.

2.4. Rigid Transformation-Movement of a 2 dimensional figure across the plane.

2.5. Rigid Motion-is a transformation which preserves the geometrical properties of the Euclidean space. Or, the distance-preserving mappings or isometries.

3. 4.2 Classifying Triangles

3.1. Geometry often involves comparing and classifying shapes, line segments and angles. Triangles can be classified by 2 different attributes.

3.2. Acute Trianlge- is a triangle with all three angles acute (less than 90°).

3.3. Equiangular Triangle- is a triangle where all three interior angles are equal in measure.

3.4. Right Triangle- is a triangle in which one angle is a right angle (that is, a 90-degree angle).

3.5. Obtuse Triangle-is one with one obtuse angle (greater than 90°) and two acute angles.

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

3.7. Isosceles Triangle- is a triangle that has two sides of equal length.

3.8. Scalene Triangle-No equal angles and no equal sides

4. 4.3 Angle Relationships in Triangles

4.1. Relationship between measurement of the sides and angles in a Triangle: The largest interior angle and side are opposite each other.

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

4.3. Corollary-a proposition that follows from (and is often appended to) one already proved.

4.4. Interior-situated within or inside; relating to the inside; inner:

4.5. Exterior-forming, situated on, or relating to the outside of something:

4.6. Interior angle-the angle between adjacent sides of a rectilinear figure.

4.7. Exterior Angle-the angle between a side of a rectilinear figure and an adjacent side extended outward.

4.8. Remote Interior Angle-are just the two angles that are inside the triangle and opposite from the exterior angle.

5. 4.4 Congruent Triangles

5.1. A triangle with all the sides congruent is called an equilateral triangle.

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

5.3. Corresponding Sides-are proportional in similar figures

5.4. Congruent Polygons-Polygons are congruent when they have the same number of sides, and all corresponding sides and interior angles are congruent.

6. 4.5 Triangle Congruence:SSS & SAS

6.1. Triangle Rigidity- as the property of triangle in which it is "fixed" at its joints.

6.2. Included Angle- is the angle between two sides of a triangle.

7. 4.6 Triangle Congruence:ASA, AAS, & HL

7.1. Included Side- is one that links two angles together.