Categorizing Quadrilaterals Based on Their Properties · on Their Properties Okay, maybe the trapezoid is a kind of oddball of quadrilaterals, but did you know that its area formula,
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• List the properties of quadrilaterals .• Categorize quadrilaterals based upon their properties .• Construct quadrilaterals given a diagonal .
Quadrilateral FamilyCategorizing Quadrilaterals Based on Their Properties
Okay, maybe the trapezoid is a kind of oddball of quadrilaterals, but did you know that its area formula, 1 __ 2 (b1 1 b2)h, can be used to determine the area of
other polygons?
Take a parallelogram, for example. Since its bases are the same length, you can just use b to describe the length of each base.
A 5 1 __ 2 (b 1 b)h
5 1 __ 2 (2b)h
5 bh
The square, too. All three measurements (b1, b2, and h) are the same. So, change all the variables to, say, s.
A 5 1 __ 2 (s 1 s)s
5 1 __ 2 (2s)s
5 1 __ 2 ? 2s2
5 s2
Even the triangle’s area can be represented using the trapezoid area formula. Can you figure out how?
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Problem 2 now I Can See the Relationships!
1. Create a Venn diagram that describes the relationships between all of the quadrilaterals listed . Number each region and name the figure located in each region .
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Problem 4 Can you Read Joe’s Mind?
Joe is thinking of a specific polygon . He has listed six hints . As you read each hint, use deductive reasoning to try and guess Joe’s polygon . By the last hint you should be able to read Joe’s mind .
1. The polygon has four sides .
2. The polygon has at least one pair of parallel sides .
3. The diagonals of the polygon bisect each other .
4. The polygon has opposite sides congruent .
5. The diagonals of the polygon are perpendicular to each other .
6. The polygon does not have four congruent angles .