Section 6.4 Rectangles

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Section 6.4 Rectangles
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• Rectangle a quadrilateral with four right
  angles.
• Since both pairs of opposite sides are congruent
  and parallel it is also a parallelogram.
• Properties
• 1. opposite sides are congruent and parallel
• 2. Opposite angles are congruent
• 3. Consecutive angles are supplementary.
• 4. Diagonals are congruent and bisect each
  other.
• 5. All four angles are right angles.

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Ex. 1 Diagonals

• Quadrilateral RSTU is a rectangle. If RT 6x
  4 and SU 7x 4, find x.
• Diagonals are congruent so
• 6x 4 7x 4.
• X 8

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Ex. 2 Angles

• Quadrilateral ABCD is a rectangle. Find y.
• We know because
  parallel lines means alternate interior angles
  are congruent
• Substitute
• Set 0
• Factor
• Solve
• Throw out y -1 because that means angle 0

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Ex. 3 Angle

• Quadrilateral LMNP is a rectangle. Find x.
• All angles are right angles
• 5x 8 3x 2 90
• X 10

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Ex. Coordinate plane
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• P. 344 7 21, 24 29, 46, 47, 49 - 52