Download Parallelogram

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ATTACH THIS TO DIALOGUE 5
Properties of Parallelograms
4/24/09
We have seen that a parallelogram has ½-turn symmetry. Use this property of parallelograms and the
diagram below to complete the equivalency groups below.
I. Equivalency Groups: Create a list of the features that are equal/congruent to the given feature.
1. a =
2. b =
3. n =
4. o =
5. e =
6. f =
7. k =
8. h =
9. AB =
10. DA =
11. CE =
12. DE =
13.
BEA =
14.
DEA =
15.
CAD =
16.
DAB =
II. Find a relation from the diagram that is an example of the given mathematical reason.
1. In a parallelogram the diagonals bisect each other.
2. In a parallelogram the opposite angles are equal.
3. A diagonal of a parallelogram cuts it into two congruent triangles.
4. Two consecutive angles in a parallelogram sum to 180.
5. In a parallelogram the opposite sides are equal.
6. Alternate interior angles are equal.
III. So far we have seen that an isosceles triangle and a parallelogram each only have 2 symmetries in
their symmetry group (the identity and reflection, or the identity and ½-turn). Notice that their
symmetry multiplication tables look very similar. Do you think that every figure with only two
symmetries (the identity and something else) will always have a multiplication table like the isosceles
triangle and parallelogram? Why or why not? (MULTIPLE SENTENCES)