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Q&A #3291


Triangle Congruence Activity

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From: Marielouise (for Teacher2Teacher Service)
Date: Mar 24, 2000 at 13:16:13
Subject: Re: Triangle Congruence Activity

I have done several searches and haven't come up with too much that is
already prepared for you.

http://math.rice.edu/~lanius/Geom/

is a site for lesson plans in geometry at Rice University.

http://mathforum.org/dr.math/problems/soarees12.13.97.html

is an answer about congruence.

http://mathforum.org/teachers/high/lessons-collections.html

is a collection of lesson plans at the Math Forum.

You were asking for a "stimulating activity" to teach congruence.  I suggest
that students cut out on heavy weight paper a triangle.  Label it and measure
it.  Trace the triangle on a paper and label the paper.  Then perform the
various transformation of

1. reflection over a horizontal line, over a vertical line, over one side of
the triangle.  Each time draw the new triangle and label it.

2.  choosing one point (vertex) of the triangle rotate the triangle around
the point until it no longer covers the original triangle.  Trace the new
triangle and label it.

3.  slide the triangle horizontally, vertically, an angle until the template
no longer covers the original triangle.  Trace the new triangle and label it.

4.  Combine any two or three of the above and find the new triangle.

Having done this, I suggest that you have templates all the same size to give
to students and a work sheet.  On the sheet indicate which is the original
triangle.  Ask for each other congruent triangle that is on the page what
transformation was done to the original triangle to arrive at the new one.
Write the answer.

Having done the above.  Give the template and questions.  Which of the
triangles shown would be congruent to the original by a stated
transformation.  If the new triangles are labeled with different labels, ask
the students after choosing the new triangle that they write the parts that
are congruent.

For many children congruency is a part of seeing.  Their visual 'gymnastic'
ability is not well developed.  I once was told that a triangle was not a
right triangle, even though it had a right angle in it, because it was facing
left and not right.  That incident has stayed with me for years!

-Marielouise, for the Teacher2Teacher service

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