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Geometry, Yellow and Blue sections were done by Chandler. Green and Orange…

- - - - Acute Angle
      - Right Angle
      - Obtuse Angle
    - - These angles are congruent because they are the same shape and size.
  - - - A line is an infinite amount of points lined up extending in two directions.
    - - Line segments are sections of lines. They have two points on both ends, and are the only types of lines that are measurable.
    - - Rays are lines that start at one point and continue in one direction infinitely.
- - - - When Transversals cross parallel lines, the transversal often creates:
        
        Supplementary Angle Pairs
        
        Angles 3 and 5 in the image are Supplementary Angles, which add up to 180 degrees and are on the same side of the transversal.
        
        Corresponding Angles
        
        Angles 2 and 6 in the image are Corresponding Angles, which are angles that have equal measures, and are on the same side of the transversal, but are not both exterior or interior angles.
        
        Vertical Angle Pairs
        
        Angles 1 and 3 in the image are Vertical Angles, which are equal angles on the opposite sides of the parallel line and transversal.
        
        Alternate Interior Angles
        
        Angles 4 and 5 in the image are Alternate Interior Angles, which have equal angle measures and are on different sides of the transversal. They are also on the inside of the two parallel lines, so the angles are interior angles.
        
        Alternate Exterior Angles
        
        Angles 2 and 7 in the image are Alternate Exterior Angles, which have equal angle measures and are on different sides of the transversal. They are also on the outside of the two parallel lines, so the angles are exterior angles.
  - - - When transversals cross non-parallel lines, the transversal doesn’t create any angle pairs that are equal or add up to 180 degrees.
- - - - The formula of a rotation is:
        90° clockwise rotation: (x,y) —> (y,-x)
        90° counterclockwise rotation: (x,y) —> (-y,x)
        180° clockwise and counterclockwise rotation: (x, y) —> (-x,-y)
        270° clockwise rotation: (x,y) —> (-y,x)
        270° counterclockwise rotation: (x,y) —> (y,-x)
        
        More about Rotations:
        
        Rotations are isometric
        
        180 rotations are equal to a reflection through its origin.
  - - - Formula of reflection: (x,y)→(−y,−x)
        Ex: (5,3) = (3,5)
        x-axis: (x, -y)
        y-axis: (-x, y)
        line y=x: (y, x)
        
        More about Reflection:
        
        Through Origin: (x,y) —> (-x,-y)
        
        x-axis: (x,y) —> (x,-y)
        
        y-axis: (x,y) —> (-x,y)
        
        y=x: (x,y) —> (y,x)
        Reflections are isometric
  - - - The formula of a Translation is:
        (x, y) —> (x ± h, y ± k)
        
        More about Translations:
        
        Two composite reflections over parallel lines is how you get a translation.
        
        They are isometric and preserve orientation
  - - - The formula to dilate an object is to multiply the x-coordinate and the y-coordinate of the points by the scale factor.
        
        More about Dilation:
        
        Not isometric
        
        Multiply distances from points by scale factors.
- - - - Theorems
        
        SAS
        
        The Side-Angle-Side Theorem states that if two sides and an angle of one triangle are congruent to another triangle’s two sides and angle, then the triangles are congruent.
        
        ASA
        
        The Angle-Side-Angle Postulate states that if two angles and one included side of a triangle are congruent to another triangle’s two angles and included side, then the triangles are congruent.
        
        SSS
        
        The Side-Side-Side Theorem states that if all three sides of a triangle are congruent to another triangle, then the triangles are congruent.
        
        AAS
        
        The Angle-Angle-Side Theorem states that if two angles and a non-included side of a triangle are congruent to another triangle’s two angles and non-included side, then the triangles are congruent.
        
        RHS
        
        The Right Angle-Hypotnuse-Side Theorem states that if the length of the hypotenuse and one side of one triangle is equal to the length of the hypotenuse and side of the other triangle, then the two triangles are congruent.