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 ?
_________________