RotationsRotate 90⁰ Clockwise: (x,y)→(y,-x)Rotate 90⁰ Counterclockwise:(x,y)→(-y,x)180⁰ Rotation:(x,y)→(-x,-y)

ReflectionsReflect across x-axis: (x,y)→(x,-y)Reflect across the y-axis: (x,y)→(-x,y)

TranslationsCoordinate Notation Example: (x+3, y-2)Means slide 3 units right and 2 units down

Alternate interior angles: [ 2 and 7] , [ 6 and 3] ∠ ∠ ∠ ∠ Pairs are CONGRUENT

Alternate Exterior angles: [ 1 and 8] , [ 5 and 4] ∠ ∠ ∠ ∠ Pairs are CONGRUENT

Corresponding Angles: [ 1 and 3] , [ 2 and 4] , [ 5 and 7] , [ 6 and 8] ∠ ∠ ∠ ∠ ∠ ∠ ∠ ∠ Pairs are CONGRUENT

Vertical Angles: [ 1 and 6] , [ 5 and 2] , [ 3 and 8] , [ 4 and 7] ∠ ∠ ∠ ∠ ∠ ∠ ∠ ∠ Pairs are CONGRUENT Same Side Interior: [ 2 and 3] , [ 6 and 7] ∠ ∠ ∠ ∠ Pairs are SUPPLEMENTARY

Exterior Angle Theorem: the measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles. m CBD = m CAB + m ACB∠ ∠ ∠

The sum of the angle measures in a triangle are equal to 180⁰m A + m B + m C = 180⁰∠ ∠ ∠

Note CardTranslations

Coordinate Notation Example:

(x+3, y-2)Means slide 3 units right and

2 units down

(x, y+4)Means don’t change the x

values, but the y values need to go up 4 units

Reflections

Reflect across x-axisPoints (x,y)→(x,-y)This means keep the x value the same and switch the sign of the y

Reflect across the y-axisPoints (x,y)→(-x,y)This means keep the y value the same and switch the sign of the x

Rotations

Rotate 90⁰ ClockwiseFlip the order of the pointsThen switch the sign of the second number (the new y value is multiplied by -1)(x,y)→(y,-x)

Rotate 90⁰ CounterclockwiseFlip the order of the pointsThen switch the sign of the first number (the new x value is multiplied by -1)(x,y)→(-y,x)

180⁰ RotationSwitch the sign of both the x and y coordinate(x,y)→(-x,-y)