Download Patty Paper Geometry

Patty Paper Geometry
Isosceles Triangle Investigation
the Conjecture & it’s Converse
Step 1: Draw line segment on your patty paper. Then label each
end point A B. Have each member of your study
group make a different length for segment AB.
Step 2: Place the “pointed end” of a compass A and then use
the pencil end to scribe an arc above the AB.
A
B
Step 3: Without changing the compass, repeat step 2 by scribing
an arc at point B.
Step 4: Connect Point A to the intersection of the arcs, and then
do the same for point B. You should be forming a
triangle. Label the top point “C”
C
A
B
What kind of Triangle have you formed? ____________
First some definitions!
Vertex Angle
Each Isosceles Triangle has a few
specially named components as
Base Angle
shown here:
Base Angle
Base
Step 5: Fold the patty paper so that point A “folds on to” point B
and segment AB folds on itself. Crease the patty paper
down the fold line. Where the fold line intersects the
base of segment AB, label it point D.
C
A
D
B
Points to Ponder !
o What do you observe?
o What do you notice about the base angles?
o Is the same thing true for every isosceles triangle that
your study group made?
Write a Conjecture:
Complete the sentence with a conjecture about an isosceles triangle:
The Base Angles of an Isosceles triangle are __________________ .
(this is called the Isosceles Triangle Postulate)
PP Isosceles Triangles
1
revised: 10/16/2013
Patty Paper Geometry
PART 2
You just discovered the postulate that says if given an isosceles triangle, then its base angles
are congruent. Do you think that if the angles are congruent you might form an isosceles
triangle? This is called the Converse of an isosceles triangle. Let’s test it.
Step 6: On a piece of patty paper, draw an angle and label it  A.
On a second piece of patty paper, trace the angle and
label it  A. (these should be congruent angles)
Step 7: Rotate or flip the second piece of patty paper so that you
move the angle  B (the one you traced) so that it is
now located over  A and the two angles help form a
triangle. To do this make sure that one pair of rays from
each angle overlap.
B
A
B
A
Step 8: With a third piece of patty paper, trace the triangle that is
formed and repeat the fold of this triangle that was done
in part one of this activity.
Points to Ponder !
 When you folded the triangle, what do you notice about the
side of the triangle?
Write a Conjecture:
Complete the sentence with a conjecture about an isosceles triangle:
If two angles of a triangle are congruent, then two sides are __________________ .
(this is called the Converse of the Isosceles Triangle Postulate)
PART 3
Use the first patty paper you folded. It’s the one in which you folded the patty paper through the
vertex angle of the isosceles triangle. Study and compare the segments AB and the fold line
CD. Measure them with a piece of patty paper or use a ruler and a protractor if you’d like.
 What type of angle is CDA ? What about CDB ?
 How are segments AD and BD related?
Write a Conjecture:
Complete the sentence with a conjecture about the “folded” segment in an isosceles
triangle:
The Fold line CD is the _______________________________ of the base of
Isosceles triangle ABC.
PP Isosceles Triangles
2
revised: 10/16/2013