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Patterns, Functions, and Algebra
Session 8 Part A Part B Part C Homework
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Session 8 Materials:

Session 8:

Problem H1


Draw any triangle on your paper. Find the three midpoints and connect them in order. Explain why the four triangles created are all similar to the original.

Problem H2


In Problem H1, how do the sides of the new triangles compare to the sides of the original? How do their areas compare?


Problem H3


Draw a square on your paper. Then draw a square with sides 3 times as long. How many times will your original square fit inside the new square?


Problem H4


If two polygons are similar, and one has sides that are r times as long as the sides of the other, how will their areas compare? Explain your answer.


Problem H5


Suppose that a tree's shadow is 21 feet long and a yardstick's shadow is 18 inches long. Using the method from Problem B3, find the height of the tree.

Suggested Reading:

Schifter, Deborah (February, 1999). Learning Geometry: Some Insights Drawn from Teacher Writing. Teaching Children Mathematics, 5, (5), 360-366.
Reproduced with permission from Teaching Children Mathematics. Copyright © 1999 by the National Council of Teachers of Mathematics. All rights reserved.

Download PDF File:
Learning Geometry: Some Insights Drawn from Teacher Writing

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