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Similar Polygons
The yearbook staff is working hard to document the memories that have been made this
year at DHS, from the basketball team’s journey to state to Dancing with the Teachers.
The pictures are currently 3.5 inches wide by 5 inches long. The staff wants to keep the
quality of the pictures but enlarge them, so they know the shape needs to be similar. If
the width of the enlargement is 8 inches wide, what does the length of the picture need
to be?
To help out the yearbook staff, we need to use similar polygons. To investigate similar
polygons, we are going to use Geometer’s Sketchpad.
Open up Geometer’s Sketchpad to a blank page.
1.
2.
3.
4.
5.
6.
7.
Select the point tool and construct four points (you are making a quadrilateral).
Next, under the line tool, select line segments, and connect the points.
Construct another point outside the polygon.
Double-click on this point. This marks the point as center.
Select the line segment tool and construct two segments of different length.
Select the segments. Then go to transform, and choose mark segment ratio.
Next, select the polygon by selecting the sides and in the transform menu choose
Dilate.
STOP. Look to your instructor for further instruction.
What happens when you drag the point marked as center? (Write two to three
sentences.)
8. Selecting three points of your quadrilateral in order. Under the measure toolbar,
select angle. A box should pop up with the measure of the angle. Record your
findings below and repeat for all angles. (Total of 8)
QUAD 1
QUAD 2
STOP.
What do you notice about the angle measures of the two quadrilaterals?
Derived from Exploring Geometry with The Geometer’s Sketchpad , ©2002 Key Curriculum Press (p. 169)
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Switch places with your partner. The writer will now be on the computer, and the
partner working on the computer will now be writing.
9. Select a segment, then under measure, select length. Record your findings on
the next page. Repeat for each side.
QUAD 1
QUAD 2
STOP. Look to instructor for next set of instructions.
Write the corresponding sides of your quadrilaterals below. (There should be four
statements)
EX. Side AB corresponds to side EF
1.
2.
3.
4.
10. Next select one side of Quad 1 and the corresponding side of Quad 2. Under
measure, chose ratio. Record and repeat for all pairs of corresponding sides.
Ratio of Side Lengths
1. Side
Side
=
2. Side
Side
=
3. Side
Side
=
4. Side
Side
=
STOP. Look to your instructor for further details.
What do you notice about the ratios? Explain in complete sentences.
11. Drag a point of one of quadrilaterals. Experiment with dragging different points
of the quadrilaterals.
Derived from Exploring Geometry with The Geometer’s Sketchpad , ©2002 Key Curriculum Press (p. 169)
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What happened when you dragged a point of one quadrilateral? What is the result for
the angles? The ratios?
Using your observations, write a definition of similar polygons:
Now, let’s use what we have just discovered to help out the yearbook staff. Find the
length that the photos need to be enlarged to, to keep the high quality of the pictures.
Show your work below!
Derived from Exploring Geometry with The Geometer’s Sketchpad , ©2002 Key Curriculum Press (p. 169)
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