February 04, 2016
Unit 8 Lesson 7
Special Parallelograms,
part 2
"You may be disappointed if you fail,
but you are doomed if you don't try."
- Beverly Sills
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How can we prove a quadrilateral is a rhombus?
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How can we prove a quadrilateral is a rectangle?
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Ways to show a quad. is a rhombus:
1. Show it has 4 congruent sides (definition)
2. Show it is a parallelogram and has 2 consecutive congruent sides (theorem 5-17)
3. Show it is a parallelogram and has perpendicular diagonals.
4. Show it is a parallelogram and has diagonals that bisect the angles.
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Ways to show a quad. is a rectangle:
1. Show it has 4 right angles. (definition)
2. Show it is a parallelogram and has congruent diagonals.
3. Show it is a parallelogram and has one right angle.
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Square
- A quadrilateral with 4 right angles and 4 congruent sides.
Why is every square a parallelogram?
Why is every square a rhombus?
Why is every square a rectangle?
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A polygon that is equilateral and equiangular is calledregular polygon.
The square is the regular quadrilateral.
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What do we need to do to show a quad. is a square?
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Example 1: Give the best name for the parallelogram.
a)
b)
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c)
d)
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Example 2
If the diagonals of a quad. are perpendicular
and congruent, must it be a square?