Discovering Discovering Parallelograms Parallelograms

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$By: Melissa Hanel Math B/Grade 11 5 Day Unit Plan Technologies ...$

#3. Repeat step #2 process to draw another circle, with center at B and radius BA. #4. Plot a point at the intersection of the two circles. Label this point D. #5. Construct a line through •D that is parallel to AB. #6. Draw segment AD. #7. Construct a line through B, parallel to AD. Then plot a point at the intersection of •B and this line. D C A B #8. Construct segment DC. Hide the circles and line DC. D C A B 18
#9. Measure and record the length of each side to verify that it is a rhombus. AB = ________, BC = ________, CD = ________, DA = ________. #10. Measure each angle: m∠ABC = ______, m∠BCD = ______, m∠CDA = ______, m∠DAB = ______. #11. Construct diagonals AC and BD. Plot point E at their intersection. D C #12. Measure the lengths of each segment formed by the diagonals. E DE = ______ EB = ______ AE = ______ EC = ______ #13. Measure the angles formed by the diagonals. Record your findings: A B m∠DEC = ______ m∠CEB = ______ m∠BEA = ______ m∠AED = ______ Make a conjecture about the diagonals of any rhombus: ______________________________________________________________ ______________________________________________________________ Test your conjecture by dragging an angle. As the sides of the rhombus become larger (or smaller), does your conjecture about the angles hold true? How could you use your segment lengths (in steps #9 and #12) to verify your conjecture algebraically (ie. using a theorem or formula)? To show that your conjecture is true, demonstrate the algebraic steps below: 19
Page 1 and 2: Discovering Parallelograms by Mary
Page 3 and 4: G.R.P.9 Apply inductive reasoning i
Page 5 and 6: III. Trapezoids 1. Properties a. ba
Page 7 and 8: POLYGON ACTIVITY I. INTERIOR ANGLES
Page 9 and 10: II. EXTERIOR ANGLES: Triangle ∠6
Page 11 and 12: IV. Assignment: pg. 415, problems #
Page 13 and 14: 12. Hide the original lines: F5Ψhi
Page 15 and 16: 8. Construct diagonal BC (follow th
Page 17: • Each student will construct and
Page 21: Day #2: Now that you have construct

Discovering Discovering Parallelograms Parallelograms

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