Triangle Congruency

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Triangle Congruency by Mind Map: Triangle Congruency

1. 4-1 Drawing, Identifying and Describing the transformations in the coordinate plane.

1.1. Something to keep in mind with reflections is that repeated reflections can create any reflections of any section over a line through the left or right side of the section.

1.2. Isometry is a transformation that preserves length, angle measure and area.

1.2.1. Another name for isometry is rigid transformation.

2. 4-2 Classifying triangles by their angle measures and side lengths.

2.1. You classify angles 2 ways.

2.1.1. Angles: Acute, Right, Obtuse, Equilanguar.

2.1.1.1. Obtuse Angle: One obtuse angle.

2.1.1.2. Right Triangle: One right angle.

2.1.1.3. Acute Angles: Has 3 acute sides,

2.1.2. Sides: Equilateral, Isosceles , Scalene.

2.1.2.1. Isosceles Triangle: At least 2 congruent sides.

2.1.2.2. Equiangular Triangle: 3 congruent sides.

2.1.2.3. Scalene Triangle: No congruent sides.

2.2. Something to remember is that when looking at a figure, you can't assume segments are congruent based on appearance. They have to be marked as congruent.

3. 4-3 Finding the measures of interior and exterior angles.

3.1. Auxiliary Line: A line that is added to a figure aid in a proof.

3.2. Corollary: A theorem whose proof follows directly from another theorem.

3.3. Interior: The set of all points inside the figure. Exterior: The set of all points outside the figure.

3.3.1. Interior Angle: Formed by 2 sides of a triangle.

3.3.2. Exterior Angle: Formed by 1 side of the triangle and extension of an adjacent side.

3.4. A remote interior angle is not adjacent to the exterior angle.

4. 4-4 Using properties of congruent angles.

4.1. Corresponding angles and sides of congruent triangles are polygons with an equal number of sides.

4.2. A helpful hint is that 2 vertices that are the endpoints of a side are called consecutive vertices.

4.3. To name all congruent corresponding parts you have to identify all pairs of corresponding congruent parts.

5. 4-5 Applying SSS & SAS to construct triangles ad solve problems.

5.1. Triangles rigidy gives you a shortcut for proving 2 triangles congruent.

5.1.1. Something to remember is that adjacent triangles share a side, so you can apply the Reflexive Property to get a pair of congruent parts.

5.2. An included triangle is an angle formed by 2 adjacent sides of a polygon.