Under Construction Day 1

Create a circle with radius AB using the compass tool.

Now use the segment tool to create another radius inside the circle. Answer question 2 on your handout.

Explore part 1:

[list=1][*]Using your compass, construct a circle that has a center at point B and a radius AB. [/*][*]Construct a congruent circle with a center at point A and a radius AB.[/*][*]Use the segment tool to connect the top and bottom points where the two circles intersect.[/*][*]Answer question 1-2 on the Explore part of your handout.[/*][/list]

Explore part 1 (Continued)

For each regular polygon, use your compass to construct a circle with the same center as the polygon and through all the vertices of the polygon. Be sure to mark a point on one of the vertices of the polygon!

Explore part 2: Construct a Rhombus

Knowing what you know about circles and line segments, think about how you might locate point D on the ray in the diagram given below, so the distance from B to D is the same as the distance from B to A? Answer question 1 on your handout by describing how you can locate this point. Hint: USE YOUR WORK FROM YESTERDAY!

Construct the new point described above using the compass tool. Then use the segment tool to connect B to D.

Now that we have three of the four vertices of the rhombus, we need to locate point E, the fourth vertex. Answer question 2 then construct point E below. HINT: First repeat your steps for constructing point D.[br]

Explore part 3: Construct a Perpendicular Bisector of a Segment and a Square (a rhombus with right angles)

Think about the only difference between a rhombus and a square....[br][br]We will begin by constructing a perpendicular bisector of a line segment. *Hint: Use part 1!

Construct the perpendicular bisector of the line segment below and put a point C on the midpoint of RS.

Using RC as one side of the square, and the perpendicular line drawn through the point C as the beginning of the square, finish constructing this square on the diagram above. (Hint: Remember that a square is also a rhombus and you have already constructed a rhombus in the first part of the lesson.)