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Pythagorean Theorem

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DISTANCE Formula (finding the distance between 2 points)

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DISTANCE Formula (finding the distance between 2 points)

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AREA and PERIMETER of figures in the coordinate plane.

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AREA and PERIMETER of figures in the coordinate plane.

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Naming, Classifying, and Measuring Angles

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Naming, Classifying, and Measuring Angles

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Use all Geometry definitions and postulates, as well as any "algebraic" properties:

Distributive Property
Combine Like Terms
Simplify
Substitution
Addition Property of Equality
Subtraction Property of Equality
Multiplication Property of Equality
Division Property of Equality

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Angle Pairs (formed with Parallel lines and transversal)

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Angle Pairs (formed with Parallel lines and transversal)

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Translations ("slides")
Reflections ("flips")
Rotations ("turns")
Dilations ("shrinks/enlarges")*
*Dilations will not be covered until
Semester 2

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figure slides left/right and or up/down

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figure flips over any axis or line in a coordinate plane

RULES
y-axis:  (x , y) --> ( -x , y )
x-axis:  (x , y) --> ( x , -y )
y = x:  (x , y) --> ( y , x )
y = -x:  (x , y) --> ( -y , -x )
horizontal line (such as y = 3 ):  only the x stays the same
vertical line (such as x = 2 ):  only the y stays the same

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figure turns about the origin (or another specified point)

RULES for Counter-Clockwise Rotations about the origin:
90 degrees:  (x , y) --> ( -y , x )
180 degrees:  (x , y) --> ( -x , -y )
270 degrees:  (x , y) --> ( y , -x )

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(*Dilations will not be covered until
Semester 2)

A figures size is reduced or enlarged. The shape of the figure stays the same... the new figure (the "Image") is still proportional to the original figure (the "Pre-Image").

"k" represents the SCALE FACTOR (the value that the Pre-Image is multiplied by to get to the Image)

If k < 1, the new figure (Image) will be smaller (a REDUCTION of the PRE-Image)

If k > 1, the new figure (Image) will be larger (an ENLARGEMENTof the PRE-Image)

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"Shortcuts" for proving two triangles are CONGRUENT:

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"Shortcuts" for proving two triangles are CONGRUENT:

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SSS  (Side-Side-Side)
SAS  (Side-Angle-Side)
ASA (Angle-Side-Angle)
AAS (Angle-Angle-Side)