Polygons

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Polygons
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Definitions

• Theorem if a parallelogram Is a rectangle, then
  its diagonals are congruent.
• Theorem if the diagonals of a parallelogram are
  congruent, then the parallelogram is a rectangle.

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Example Definition

• A Rectangle is a quadrilateral with four right
  angles. It follows that since both pairs of a
  opposite angles are congruent, a rectangle is a
  special type of parallelogram.

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The Mazdrons are building an addition to their
house. Mr. Mazdron is cutting an opening for a
new window. If he has measured to see that the
opposite sides are congruent and that the window
opening is a rectangle?Example on next page ..
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Example

• Explore drew a diagram and label the vertices
  of the window opening a, b, c, and d. According
  to Mr. Mazdrons measurements, segment AB
  segment CD, segment BC segment AD, and
  segment AC segment BD.
• Plan We can show that ABCD is a rectangle by
  first probing that it is a parallelogram and then
  probing that it has four right angles.
• Continue.. of the example

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Example continued..

• Solve
• Given AB CD
• BC AD
• AC BD
• Prove ABCD is a rectangle