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Unit 5 Quadrilaterals - Coggle Diagram

- - - - Sides: AB = CD, AD = BC, AB || CD, AD || BC
      - Angles: m<A = m<B = m<C = m<D
        
        Definition of rectangle: If a quadrilateral has 4 right angles, then it is a rectangle.
        
        A rectangle is a parallelogram with one right angle.
      - Diagonals: AO = CO, BO = DO, AC = BD
        
        If diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.
      - Symmetry: Point and line symmetry
  - - - Angle: A = C, B = D
      - Diagonals: AO = CO, BO = DO, AC perpendicular to BD
        
        If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus.
      - Sides: AB = CD = BC = DA, AB || CD, AD || BC
        
        Definition of a rhombus-- A rhombus is a quadrilateral with all four sides congruent.
        
        If two consecutive sides of a parallelogram are congruent, then it’s a rhombus.
      - Symmetry: Point and line symmetry
  - - - Angles: m<A = m<B = m<C = m<D = 90
        
        Definition of a square-- A square is a quadrilateral with four congruent sides and four right angles.
        
        If a rhombus has a right angle, it is a square.
      - Sides: AB = CD = BC = DA, AB || CD, AD || BC
        
        Definition of a square-- A square is a quadrilateral with four congruent sides and four right angles.
        
        If 2 consecutive sides of a rectangle are congruent, it is a square
      - Diagonals: AO = CO, BO = DO, AC = BD, AC perpendicular to BD
      - Symmetry: Point and line symmetry
      - Proof: If a parallelogram has 2 consecutive sides are congruent and a right angle, then it is a square.
- - - - Definition of parallelogram—If both pairs of opposite sides of a quadrilateral are parallel, then the quadrilateral is a parallelogram
    - - If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
    - - If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
      - If one pair of opposite sides of a quadrilateral are parallel and congruent, then the quadrilateral is a parallelogram.
- - - - A midsegment of a triangle is parallel to the third side and is half as long as it.
  - - - The centroid of a triangle is located two thirds of the distance from a vertex to the midpoint of the side opposite the vertex on a median.