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Rotations Rotate 90⁰ Clockwise: ( x,y )→(y,-x) Rotate 90⁰ Counterclockwise:( x,y )→(- y,x )

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

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Rotations Rotate 90⁰ Clockwise: ( x,y )→(y,-x) Rotate 90⁰ Counterclockwise:( x,y )→(- y,x )

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  1. 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 areCONGRUENT 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 Rotations Rotate 90⁰ Clockwise: (x,y)→(y,-x) Rotate 90⁰ Counterclockwise:(x,y)→(-y,x) 180⁰ Rotation:(x,y)→(-x,-y) 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 180⁰ m∠A + m∠B + m∠C = 180⁰ Reflections Reflect across x-axis: (x,y)→(x,-y) Reflect across the y-axis: (x,y)→(-x,y) Translations Coordinate Notation Example: (x+3, y-2) Means slide 3 units right and 2 units down

  2. Rotations Rotate 90⁰ Clockwise Flip the order of the points Then switch the sign of the second number (the new y value is multiplied by -1) (x,y)→(y,-x) Rotate 90⁰ Counterclockwise Flip the order of the points Then switch the sign of the first number (the new x value is multiplied by -1) (x,y)→(-y,x) 180⁰ Rotation Switch the sign of both the x and y coordinate (x,y)→(-x,-y) Reflections Reflect across x-axis Points (x,y)→(x,-y) This means keep the x value the same and switch the sign of the y Reflect across the y-axis Points (x,y)→(-x,y) This means keep the y value the same and switch the sign of the x Note Card 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 Translations

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