Angle Relationships and Transformations

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Complementary Angles

Two angles whose sum is 90 degrees.

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Supplementary Angles

Two angles whose sum is 180 degrees.

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Vertical Angles

A pair of opposite congruent angles formed by intersecting lines.

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Interior Angles

Angles inside a polygon.

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Exterior Angles

Angles on the outside of a polygon by extending the sides of the polygon.

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Sum of Interior Angles Formula

(n-2)⋅180°

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360°

Sum of Exterior Angles

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Transversal

A line that intersects two or more lines.

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Corresponding Angles

Two congruent angles in matching positions on two parallel lines cut by a transversal.

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Alternate Interior Angles

Two congruent angles that lie within two parallel lines and on opposite sides of the transversal.

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Alternate Exterior Angles

Two congruent angles that lie outside two parallel lines and on opposite sides of the transversal.

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Same-side Interior Angles

Two supplementary angles that lie within two parallel lines and on the same side of the transversal.

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Same-side Exterior Angles

Two supplementary angles that lie outside two parallel lines and on the same side of the transversal.

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Measure of an interior angle of a regular polygon

(n-2)⋅180°÷n

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Measure of an exterior angle of a regular polygon

360°÷n

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Transformation

A change made to the location or the size of a figure.

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Image

The new figure formed from a transformation.

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A'

Prime notation to identify the image point.

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Translation

A transformation in which the figure slides.

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Coordinate Notation

(x,y) -> (x + 7, y - 4)

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Tessellation

Covering a plane (piece of paper) with repeating pattern of one or more shapes with no gaps or overlaps.

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180°

A tessellation can be created with a polygon whose adjacent angles add to __________.

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Reflection

A transformation in which the figure is flipped over a line.

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Line of Symmetry

A line that divides the figure into two reflecting parts.

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Rotation

A transformation in which a figure is turned about a fixed point.

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Rotational Symmetry

A figure that when rotated, looks the same as the original.

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Order of Rotational Symmetry

How many matches a figure has of itself as it is rotated once 360°.

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Dilation

A transformation that shrinks or enlargens with respect to a fixed point.

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Scale Factor

The ratio of the image to the original figure.

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Dilation Notation

(x,y) -> (kx, ky), Given k, the scale factor such that k>0

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Shrink

0<Scale Factor<1

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Enlargen

Scale Factor>1

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Reflection of x-axis

(x, -y)

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Reflection of y-axis

(-x,y)

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Reflection of y=-x

(-y,-x)

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90° Clockwise rotation about the origin

(y, -x)

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90° Counterclockwise rotation about the origin

(-y,x)

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180° Rotation about the orgin

(-x,-y)