Name_______________________________
Geometry Period_____
2-6 Notes
Date______
Lesson 2-6: Constructing a Square
Today’s Goal: How do I construct a square with a given side length?
Warm-up
List the properties of a square. With your shoulder partner, discuss how these properties
can be used in the construction of a square.
Properties of a
Square
Construction(s) that would lead
to this property
Visualize
Constructing a Square
1. Extend line segment AB using a straightedge on side A.
2. Construct the perpendicular line at point A (just like yesterday’s class)
3. Measure the distance from A to B with your compass.
4. Needlepoint on A; swing arc above the line segment to mark distance of
AB. Mark the intersection of this arc with the perpendicular line. Label D. (extend perpendicular line with
straightedge if necessary)
5. Needlepoint on B; swing arc above the line segment to mark distance of AB.
6. Needlepoint point C; swing compass to cross at the arc made in step 5. Label the intersection C.
7. Draw segment CD and BC. Done!
Let’s Construct!
Using only your compass and a straight edge, construct a square with side length XY:
You Try!
Using only your compass and a straight edge, construct a square with side length AB:
Are you Ready to move
on?
Putting it all together
Harrison High School is looking to build a room that inspires creativity in students! For the “Math
Center,” there are certain requirements that the builders must satisfy. YOU are the builder today! 
Your task: Create a floor plan of the new Math Center that has the following components. Use the
checklist as you work. Be sure to only use your compass and a straight edge to construct the items listed
below!
The desk must be a square, with any given side length. (you choose!)
Must have an inscribed hexagonal floor rug
The TV is located at the circumcenter of a triangle. Mark the TV’s location with
an “X.” (Hint: sketch a triangle of any size and finds it circumcenter)
A table must be in the shape of an equilateral triangle.
Suggestions:
*Use differ colors throughout your work!
*Use light construction marks until you are confident that you have constructed
the right objects!
*Make a rough sketch first
Name__________________________________
2-6 HW
Geometry Period______
Date______
1) The diagram to the right shows what type of construction?
a)
b)
c)
d)
Angle Bisector
Perpendicular bisector
A line perpendicular to AB and through a point
A 45 degree angle
2) Construct an inscribed square using segment AB.
3) Jack, the puppy shown to the right, decided to bury his bone in the back yard of
the Smith’s house. The Smiths were very upset about this and asked you to find
and remove the bone from their yard - the only problem is that no one knows
where exactly it is. You take your best guess and try digging in the exact
opposite corner of the cat’s play area and perpendicularly to the house.
How can you use a construction of a square to find the bone’s location?
Leaving all your construction marks, use the diagram below to locate where you might start digging.
4)
Think about it! Then, write about it!
If I construct an inscribed square with the segment AB (to the right) and then a square with side length AB (the
second method we learned), which square would have a bigger area? Explain your work! Sketch if it helps you!