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G.CO.D.12 ACTIVITY #3 – geometrycommoncore NAME: ________________________ 1 THE HIDDEN RHOMBUS Why do these constructions work? Construct a Midpoint Construct a Perpendicular Line Through a Point Not on the Line Construct a Perpendicular Line Through a Point On the Line Construct an Angle Bisector 1. When performing these constructions you kept your compass at a fixed length. This creates distances that are equal - thus the 4 equal sides of a rhombus. a) Use a ruler and draw in the missing sides of the rhombus in each of these constructions. b) Shade the rhombus with your pencil. 2. In the first three constructions we needed to create lines that were perpendicular. Which property of a rhombus do you think we are using to accomplish this goal? Opposite sides are || Opposite sides are Opposite angles are Consecutive ’s = 180 Diagonals bisect each other Diagonals are Diagonals are Bisectors 3. In the angle bisector construct we need to divide an angle into two equal parts. Which property of a rhombus do you think we are using to accomplish this goal? Opposite sides are || Opposite sides are Opposite angles are Consecutive ’s = 180 Diagonals bisect each other Diagonals are Diagonals are Bisectors G.CO.D.12 ACTIVITY #3 – geometrycommoncore 2 4. Given VB -- perform the midpoint construction. This time labeling the two intersection found to be H and K. Draw in VH , VK , BH , & BK . Also draw HK . V B Why is VH = VK? _______________________________________________________________________ Why is BH = BK? _______________________________________________________________________ Why is VH = VK = BH = BK? _______________________________________________________________ What is the most specific name for the quadrilateral VHBK? _____________________________________ Will this specific quadrilateral be formed every time using this construction? Yes or No Why or why not… Label the intersection of HK and VB is point M. What is true about VM and BM? _______________________________________________________ What is true about HM and KM? _______________________________________________________ What is the measure of the angle formed at the intersection of HK and VB ? _________________