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Name: ____________________ 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)