Activity – (cont.)
Patty Papersare squares of paper that are waxed on
one side and used to separate hamburgers before they
are cooked. Since these squares crease easily and leave
a white mark when folded, they are ideal for studying geometry.
1) The shape of patty paper allows us to start right away, what can we use the corners to show?
Find the shiny, waxy side, now flip it over…
When writing, you want the un-shiny, un-waxy side!
And pencil works best!
2) Draw a segment on your patty paper, label it line p. Now fold the sheet of patty paper to construct a perpendicular line, label it m. Explain the steps of your construction.
3) Fold the sheet of patty paper to construct line n also perpendicular to line p. Write a conjecture about lines m and n.
4) Next, draw an angle on your patty paper. Fold the paper through the vertex so that the two sides coincide (in the same position). Justify why this will bisect the angle.
Hello, I’m Iggy the Iguana. I really enjoy snacking. My favorite snack… juicy flies!
When I see one, my tongue pops out of my mouth to catch it. YUM!!! Funny thing is, my tongue always comes out right down the middle. Here, let me show you what I mean…
5) What geometric figure does Iggy‘s mouth represent?
6) Angles are composed of two ______and one ______.
7) Identify the sides of the angle by name.
8) Write a geometric statement describing the angles that are congruent, given bisects .
Any point on the angle bisector is equidistant to the sides of the angle.
It’s time to chow down…
Perform the angle bisector construction to find out how many fat, juicy flies I’m having for a snack.
{Only count them when I hit their bodies, if I only get their wings the little buggers get away.}
9) How many flies will I catch at this meal?
I have to be careful hunting flies, they like to hang out by the zappers. There’s this sweet spot down the road that has three zappers. The flies really like it there and I can usually get a very filling meal when I go. Here’s the problem, those zapper’s sting and if all three get me at once it HURTS, A LOT!
10) Construct the angle bisectors of the triangle formed by the zappers to find the one place I need to avoid when hunting flies.
Hey, I am Cute little Carol. I’m a Caterpillar. But I warn you, I can be kind of CRAZY!! When you follow my directions to an upside down “T” I do a split for you.
Check me out, I’m walking down . is the perpendicular bisector of.
In order to assure that I’m folding a perpendicular bisector, I just have to line up the endpoints when I fold.
11) Write a geometric statement describing which segments are congruent, given that bisects.
12) Write a geometric statement describing the relationship between and.
13) Mark my diagram to indicate everything we know by simply having a perpendicular bisector.
14) Can a line have a bisector? Why or why not?
I’m quite a colorful character…
My first section is my head, draw in my smiley face.
What you can’t see is the line down my back.
It is formed by connecting the midpoints of my sets of legs.
15) Complete the perpendicular bisector constructions to find the midpoints of each of my sets of legs. Connect those midpoints to create the line down my back.
I’m glad my friends Cindy the Centipede and Millie the Millipede are out of town!
They are a lot of work!
Any point on the perpendicular bisector is equidistant to the ends of the segment.
Whew, all that walking and designing made me very tired; I think I’ll take a nap.
In my dreams I wake up a beautiful butterfly like my best friend Betty.
While I’m resting, check out this sketch I made…
16) Construct an angle bisector on top of each wing; do the angle bisectors intersect with my polka dots?
Dot 1) Dot 2)
17) Name each of the angles on the wings in three different ways.
Left wing:
Right wing:
18) Construct the perpendicular bisector of my spine. Is my x-mark on the midpoint of the spine?
19) Name the segment that indicates the spine in two ways.
Zzzz…
Hi, I’m Betty the beautiful Butterfly.
I fly from flower to flower, collecting nectar to eat.
One day I came across the particularly tasty looking group below:
20) Represent my path (the dotted lines in the diagram) as one continuous straight line by constructing congruent segments end-to-end.
The worst thing about flying around collecting nectar is flying into spider webs… YUCK, I HATE SPIDERS!
Although Sammy the Spider is pretty cool, we have an understanding… I stay out of his web and he doesn’t eat me.
21) Help Sammy work on his web by copying the angle three times and attaching them to what he’s already got.
Extension:
Oops, Sammy’s web has a couple holes… He needs H. E. L. P.!
22) Investigate the steps for constructing parallel lines. Construct the parallel segments through X that will complete his web home.
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