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SUPPLEMENTARY ANGLES. 2-angles that add up to 180 degrees. COMPLEMENTARY ANGLES. 2-angles that add up to 90 degrees. Vertical Angles . Vertical Angles are Congruent to each other. <1 =<3 <2=<4 <1+<2=180 degrees <2+<3=180 degrees <3+<4=180 degrees <4+<1=180 degrees.

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vertical angles are congruent to each other
Vertical Angles are Congruent to each other
  • <1 =<3
  • <2=<4
  • <1+<2=180 degrees
  • <2+<3=180 degrees
  • <3+<4=180 degrees
  • <4+<1=180 degrees
slide30

(Upside down T!!!!)

(Big Angle Small Angle!!!!!)

centroid
CENTROID

MEDIANS ARE IN A RATIO OF 2:1

parallelogram
Parallelogram
  • Opposite sides are congruent.
  • Opposite sides are parallel.
  • Opposite angles are congruent.
  • Diagonals bisect each other.
  • Consecutive (adjacent) angles are supplementary (+ 180 degrees).
  • Sum of the interior angles is 360 degrees.
rectangle
Rectangle
  • All properties of a parallelogram.
  • All angles are 90 degrees.
  • Diagonals are congruent.
rhombus
Rhombus
  • All properties of a parallelogram.
  • Diagonals are perpendicular (form right angles).
  • Diagonals bisect the angles.
square
Square
  • All properties of a parallelogram.
  • All properties of a rectangle.
  • All properties of a rhombus.
isosceles trapezoid
Isosceles Trapezoid
  • Diagonals are congruent.
  • Opposite angles are supplementary + 180 degrees.
  • Legs are congruent
prove a parallelogram1
Prove a Parallelogram
  • Distance formula 4 times to show opposite sides congruent.
  • Slope 4 times to show opposite sides parallel (equal slopes)
  • Midpoint 2 times of the diagonals to show that they share the same midpoint which means that the diagonals bisect each other.
prove a rectangle
Prove a Rectangle
  • Prove the rectangle a parallelogram.
  • Slope 4 times, showing opposite sides are parallel and consecutive (adjacent) sides have opposite reciprocal slopes thus, are perpendicular to each other forming right angles.
prove a square
Prove a Square
  • Prove the square a parallelogram.
  • Slope formula 4 times and distance formula 2 times of consecutive sides.
prove a trapezoid1
Prove a Trapezoid
  • Slope 4 times showing bases are parallel (same slope) and legs are not parallel.
prove an isosceles trapezoid1
Prove an Isosceles Trapezoid
  • Slope 4 times showing bases are parallel (same slopes) and legs are not parallel.
  • Distance 2 times showing legs have the same length.
prove isosceles right triangle1
Prove Isosceles Right Triangle
  • Slope 2 times showing opposite reciprocal slopes (perpendicular lines that form right angles) and Distance 2 times showing legs are congruent.
  • Or Distance 3 times and plugging them into the Pythagorean Theorem
prove an isosceles triangle1
Prove an Isosceles Triangle
  • Distance 2 times to show legs are congruent.
prove a right triangle1
Prove a Right Triangle
  • Slope 2 times to show opposite reciprocal slopes (perpendicular lines form right angles).
slide108

The locus of points equidistant from two points, P and Q, is the perpendicular bisector of the line segment determined by the two points.

isometry transformation that preserves distance
Isometry: Transformation that Preserves Distance
  • Dilation is NOT an Isometry
  • Direct Isometries
  • Indirect Isometries
direct isometry1
Direct Isometry
  • Preserves Distance and Orientation (the way the vertices are read stays the same)
  • Translation
  • Rotation
opposite isometry1
Opposite Isometry
  • Distance is preserved
  • Orientation changes (the way the vertices are read changes)
  • Reflection
  • Glide Reflection
slide210

CENTRAL ANGLE

m∠O = m arc-AB

A

o

B