# Similar triangles

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A. Find at least three examples of congruent objects in a typical classroom. (don't need pictures).

What out of class activities could you employ to make students aware of congruent objects?

Stan is standing on the bank of a river wearing a baseball cap. Standing erect and looking directly at the other bank, he pulls the bill of his cap down until it just obscures his vision of the opposite bank. He then turns around, being careful not to disturb the cap, and picks out a spot that is just obscured by the bill of his cap. He then paces off the distance to this spot and claims that the distance across the river is approximately equal to the distance he paced. Is Stan's claim true? Why?

A building was to be built on a triangular piece of property. The architect was given the approximate measurements of the angles of the triangular lot as 54°, 39°, and 87° and the lengths of two of the sides as 100 m and 80 m. When the architect began the design on drafting paper, she drew a triangle to scale with the corresponding measures and found that the lot was considerably smaller than she had been led to believe. It appeared that the proposed building would not fit. The surveyor was called. He confirmed each of the measurements and could not see a problem with the size. Neither the architect nor surveyor could understand the reason for the other's opinion.

1.Explain why the architect felt she was correct.

2. Why did the surveyor feel he was correct?

3. Suggest a way to provide an accurate description of the lot.

The game of Triominoes has equilateral-triangular playing pieces with numbers at each vertex, shown as follows:

If two pieces are placed together as shown in the following figure, explain what type of quadrilateral is formed:

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If you asked your elementary students:

" What other games (board games or sporting games) have any geometric components?"

1. What might they respond?

2. What activities or projects might teachers initiate around their responses?

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#### Solution Summary

Finding the thrid side of pairs of similar triangles using proportions

Similar Triangles and Finding Coordinates

Construct the quadrature of 3 squares. Let a = 3 be a line segment that extends along the y-axis from the origin O to the point B at (0,3). Let b = 4 be a line segment that extends along the x-axis from the origin O to the point A at (4,0). Let x be the hypotenuse of triangle ABO.

Let c = 2 be a line segment extending above the x-axis from point A to a point C, forming a right angle at CAB. Let d be the hypotenuse from C to B. Draw a perpendicular line to the x-axis from C that is called D.

1. Show that Triangle ABO is similar to Triangle CAD, where O is the origin.

2. Find the coordinates of C in terms of a and b.

3. Use the distance formula to find the distance of BC.

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