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A transformation is a one-to-one and onto function that maps one set of points in space to another set of points

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A transformation is a one-to-one and onto function that maps one set of points in space to another set of points

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Congruency: Congruence is defined as being able to move one figure with rigid motion (slide, rotate or reflect) so that it lies on top of the second figure​

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Congruency: Congruence is defined as being able to move one figure with rigid motion (slide, rotate or reflect) so that it lies on top of the second figure​

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Similar Figures: Figures are similar if their corresponding angles are congruent, and the ratios of the lengths of their corresponding sides are equal

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Similar Figures: Figures are similar if their corresponding angles are congruent, and the ratios of the lengths of their corresponding sides are equal

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Two angles are said to be congruent if they have the same measure

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Two angles are said to be congruent if they have the same measure

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When a side of a triangle is extended, the supplement of the angle of the triangle is called the exterior angle

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When a side of a triangle is extended, the supplement of the angle of the triangle is called the exterior angle

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When a side of a triangle is extended, the supplement of the angle of the triangle is called the exterior angle

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When a side of a triangle is extended, the supplement of the angle of the triangle is called the exterior angle

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Angle Angle Angle (AAA)​

If two angles of one triangle are respectively equal to two angles of another triangle, then the two triangles are similar.​

It is sufficient to prove that only two pairs of angles are respectively equal to each other. Because the angle sum of a triangle is always 180°, the third pair of angles will automatically be equal. ​

Side Angle Side (SAS)​

If the ratio of the lengths of two sides of one triangle is equal to the ratio of the lengths of two sides of another triangle, and the included angles are equal, then the two triangles are similar.​

Side Side Side (SSS)​

If each of the sides of one triangle can be matched up with each of the sides of another so that the ratios of matching sides are equal, then the two triangles are similar.​

Right-angle Hypotenuse Side (RHS)​

If the ratio of the hypotenuse and one side of a right-angled triangle is equal to the ratio of the hypotenuse and one side of another right-angled triangle, then the two triangles are similar.

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Two angles with a common vertex whose sides form opposite rays are called vertical angles

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Two angles with a common vertex whose sides form opposite rays are called vertical angles

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Two adjacent angles whose non-common sides are opposite rays are called a linear pair

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Two adjacent angles whose non-common sides are opposite rays are called a linear pair

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A transformation that results preserves distance (length and angles) is called an isometry or is referred to as a rigid motion

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A transformation that results preserves distance (length and angles) is called an isometry or is referred to as a rigid motion

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SSS (Side, Side, Side)​

SAS (Side, Angle, Side)​

ASA (Angle, Side, Angle)​

AAS (Angle, Angle, Side)​

RHS (Right angle-Hypotenuse-Side or the Hypotenuse Leg theorem)

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Equilateral Triangle: A triangle with three sides of equal length​

Isosceles Triangle: A triangle that has two sides of equal length​

Scalene Triangle: A triangle where all 3 sides have different lengths​

Right Triangle: A triangle where an interior angle is 90°​

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Types of Triangles based on the relationships between their sides

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Types of Triangles based on the relationships between their sides

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a scalene triangle if and only if no two sides are congruent (all sides are of differing lengths);​

an isosceles triangle if and only if at least two of its sides are congruent (the non-congruent side is called the base, and the angles enclosing the base are the base angles);​

an equilateral triangle if and only if all three sides are congruent.

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Angles and transformations all have to do with finding if triangles are congruent, similar, or neither

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Angles and transformations all have to do with finding if triangles are congruent, similar, or neither

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Congruency has to do with similarity because if 2 shapes are congruent they are similar in nature

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Congruency has to do with similarity because if 2 shapes are congruent they are similar in nature

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Similarity helps us to find different properties on similar shapes/triangles (side lengths/angle measurements) and can help us investigate many situations

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Similarity helps us to find different properties on similar shapes/triangles (side lengths/angle measurements) and can help us investigate many situations

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When thinking about the different types of triangles it helps us think through similar/congruent triangles

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When thinking about the different types of triangles it helps us think through similar/congruent triangles