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  # Bell Ringer - PowerPoint PPT Presentation
  
  Bell Ringer. Rhombi Rectangles &amp; Squares. Rhombus. Definition:. A rhombus is a parallelogram with four congruent sides. Opposite sides are parallel. Opposite sides are congruent. Opposite angles are congruent. Consecutive angles are supplementary. Diagonals bisect each other. ≡. ≡.
  
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  ## PowerPoint Slideshow about ' Bell Ringer' - jerry-cook
  
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  Presentation Transcript
  Bell Ringer
  
  Lesson 6-4: Rhombus & Square
  
  Rhombi
  
  Rectangles &
  
  Squares
  
  Rhombus
  
  Definition:
  
  A rhombus is a parallelogram with four congruent sides.
  
  • Opposite sides are parallel.
  • Opposite sides are congruent.
  • Opposite angles are congruent.
  • Consecutive angles are supplementary.
  • Diagonals bisect each other
  
  Since a rhombus is a parallelogram the following are true:
  
  Properties of a Rhombus
  
  Theorem:
  
  The diagonals of a rhombus are perpendicular.
  
  Theorem:
  
  Each diagonal of a rhombus bisects a pair of opposite angles.
  
  Rhombus Examples .....
  
  Given: ABCD is a rhombus. Complete the following.
  
  • If AB = 9, then AD = ______.
  • If m<1 = 65, the m<2 = _____.
  • m<3 = ______.
  • If m<ADC = 80, the m<DAB = ______.
  • If m<1 = 3x -7 and m<2 = 2x +3, then x = _____.
  
  9 units
  
  65°
  
  90°
  
  100°
  
  10
  
  Square
  
  Definition:
  
  A square is a parallelogram with four congruent angles and four congruent sides.
  
  • Opposite sides are parallel.
  • Four right angles.
  • Four congruent sides.
  • Consecutive angles are supplementary.
  • Diagonals are congruent.
  • Diagonals bisect each other.
  • Diagonals are perpendicular.
  • Each diagonal bisects a pair of opposite angles.
  
  Since every square is a parallelogram as well as a rhombus and rectangle, it has all the properties of these quadrilaterals.
  
  Squares – Examples…...
  
  Given: ABCD is a square. Complete the following.
  
  • If AB = 10, then AD = _____ and DC = _____.
  • If CE = 5, then DE = _____.
  • m<ABC = _____.
  • m<ACD = _____.
  • m<AED = _____.
  
  10 units
  
  10 units
  
  5 units
  
  90°
  
  45°
  
  90°
  
  Rectangles
  
  Definition:
  
  A rectangle is a parallelogram with four right angles.
  
  • Opposite sides are parallel.
  • Opposite sides are congruent.
  • Opposite angles are congruent.
  • Consecutive angles are supplementary.
  • Diagonals bisect each other.
  
  A rectangle is a special type of parallelogram.
  
  Thus a rectangle has all the properties of a parallelogram.
  
  A
  
  B
  
  E
  
  D
  
  C
  
  Properties of Rectangles
  
  Theorem:
  
  If a parallelogram is a rectangle, then its diagonals are congruent.
  
  Therefore, ∆AEB, ∆BEC, ∆CED, and ∆AED are isosceles triangles.
  
  Converse:
  
  If the diagonals of a parallelogram are congruent , then the parallelogram is a rectangle.
  
  A
  
  B
  
  2
  
  3
  
  1
  
  E
  
  4
  
  5
  
  6
  
  D
  
  C
  
  Examples…….
  • If AE = 3x +2 and BE = 29, find the value of x.
  • If AC = 21, then BE = _______.
  • If m<1 = 4x and m<4 = 2x, find the value of x.
  • If m<2 = 40, find m<1, m<3, m<4, m<5 and m<6.
  
  x = 9 units
  
  10.5 units
  
  x = 18 units
  
  m<1=50,
  
  m<3=40,
  
  m<4=80,
  
  m<5=100,
  
  m<6=40