MTH 202 – 006
Class Activity 8W
p 283 – 285
This activity is an introduction to constructions with straightedge (aka, ruler) and
compass (aka, circle-maker). You can think of these two tools as a geometric duo of
super heroes! Straightedge’s super powers are that it can connect any two points with a
line segment and can extend any line segment into a ray or a line. Compass’ super power
is that it can make a circle given any center and radius. (This may not seem like much for
Compass, but if you think about the definition of a circle, it means that he can mark lots
of points so that after Straightedge does his business there will be lots of equal segments.)
Together, Straightedge and Compass can vanquish almost any foe (as we will see on this
activity and those to come – including some on your exam).
Adventure 1: Can Straightedge and Compass construct an isosceles triangle?
Straightedge: We need to make an isosceles triangle – a triangle with at least two equal
sides. I can draw the sides of the triangle, but I need to know that two of them are
the same length.
Compass: Leave that to me! I can make a circle, and if you draw in two radii they are
guaranteed to be the same length.
THINK: Which two sides are equal and why?
Adventure 2: Can Straightedge and Compass construct an equilateral triangle?
Straightedge: Holy vertices, Compass, now we need to make an equilateral triangle – all
the sides have to be equal!
Compass: Well, I can mark off lots of equal lengths if you give me a side to start with.
A
B
Straightedge: Ok, there’s a side for you.
Compass: If I draw a circle centered at A with radius AB, then any point on that circle
will be an equal distance from A as is B. That’s the definition of circle, my flatsided amigo. But we have to make sure it is also an equal distance from B as is A.
Straightedge: Sounds like we might need another circle.
Compass: Then I will draw another circle, this time centered at B. But it will have the
same radius as the other circle – AB!
C
A
B
A
B
THINK: Why is this triangle equilateral? Why would it be hard to do this w/o circles?
THINK: Does Compass really need to draw the entire circles? If you were playing with
your own Compass action figure, how might you make it easier on yourself?
Adventure 3: Can our heroes turn a pair of equal segments into a rhombus?
C
B
A
Straightedge: This poor pair of equal segments needs to become a rhombus – we have to
add two more sides of the same length.
Compass: I keep telling you, I can mark off points of equal length – it’s called a circle!
Straightedge: Well then, mark off something at C that is equal to CA and mark off
something at B that is equal to BA..
Compass: I will make two circles, and any radius of the first circle will be equal to CA
and any radius of the second circle will be equal to BA. Since CA = BA we will just
find a spot on both circles and this will make a rhombus.
(1)
(1)
D
C
C
A
A
B
B
(2)
THINK: Is this really a rhombus?
Adventure 4: Can the super partners make a triangle that has sides of length
6 inches, 3 inches, and 2 inches?
Straightedge: Awww, Compass. We can’t do this one…it’s impossible.
Compass: Have faith, my straight-laced compadre. Remember that I can make circles!
THINK: Who is right? Why?