text: Bell Ringer
  
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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. ≡. ≡.
  
  I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
  
  ## PowerPoint Slideshow about ' Bell Ringer' - jerry-cook
  
  Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
  
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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
explanation: The document is a PowerPoint presentation slide titled "Bell Ringer" that covers definitions and properties of rhombi, rectangles, and squares. It includes several examples and questions related to these geometric shapes, with answers provided for some of the questions.
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  1 / 11
  
  # 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. ≡. ≡.
  
  I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
  
  ## PowerPoint Slideshow about ' Bell Ringer' - jerry-cook
  
  Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
  
  - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
  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
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document is a PowerPoint presentation slide titled "Bell Ringer" that covers definitions and properties of rhombi, rectangles, and squares. It includes several examples and questions related to these geometric shapes, with answers provided for some of the questions.
  
  Label: multiple-question-and-answer