Geometry Lesson 57 Pg' 294

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GeometryLesson 5-7 Pg. 294

• Proving Quadrilaterals are Parallelograms

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Theorem 5-21

• If one pair of opposite sides of a quadrilateral
  are equal and parallel, then the quadrilateral is
  a parallelogram.
• - This symbol represents a parallelogram.

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Proof for Thrm. 5-21
A
P
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• Given Quad. SOAP SP ?? OA SP OA
• Prove SOAP is a .
• Statement
  Reason
• 1. Draw PO.
  1. Through 2 pts exactly 1
  line can be drawn.
• 2. Quad. SOAP SP ?? OA SP OA
  2 . Given
• 3. ?1 ?2
  3. If 2 ?? lines are cut
  by a trans. then alt. int. ?s
• 
  are .
• 4. PO PO
  4. Reflexive Property
• 5. ?PAO ? ?OSP
  5. SAS
• 6. ?3 ?4
  6. CPCTE
• 7. PA ?? OS
  7. If 2 lines are cut by a
  trans. and alt. int. ?s are
• 
  then the 2
  lines are ??.
• 8. SOAP is a .
  8. Defn. of a .

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S
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Theorem 5-22

• If both pairs of opposite sides of a
  quadrilateral are equal, then the quadrilateral
  is a parallelogram.

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Proof of Thrm. 5-22
T
R
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• Given Quad. WATR WA RT WR AT
• Prove WATR is a
• Statement
  Reason
• 1. Quad. WATR WA RT WR AT 1. Given
• 2. WT WT
  2. Reflexive Property
• 3. ?RTW ? ?AWT
  3. SSS
• 4. ? 2 ?1 ? 3 ?4
  4. CPCTE
• 5. RT ?? AW RW ?? AT 5.
  If 2 lines are cut by a
• 
  transversal and
  alternating
• 
  interior ?s are
  then the lines
• 
  are ??.
• 6. WATR is a .
  6. Defn. of a .

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W
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Theorem 5-23

• If both pairs of opposite angles of a
  quadrilateral are equal, then the quadrilateral
  is a parallelogram.

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Theorem 5-24

• If the diagonals of a quadrilateral bisect each
  other, then the quadrilateral is a parallelogram.

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• Five ways to prove that a quadrilateral is a
  parallelogram.
• 1. Show both pairs of opposite sides parallel.
• 2. Show one pair of opposite sides parallel
• equal.
• 3. Show both pairs of opposite sides equal.
• 4. Show both pairs of opposite angles equal.
• 5. Show that the diagonals bisect each other.