Below is an introduction to congruent triangles that makes use of student prior knowledge of transformations. It also encourages students to deduce information from a diagram and to justify their reasoning (and for fun, when we deduce something, we'll say "I spy ____". Totally wishing for some prop like a monacle on a popsicle stick!)
Show students the following diagram, and go through the steps below. Some questions/prompts are shown in blue.
1. What
type of transformation is shown in this diagram?
2. Reveal the
measures of ABC. Ask students, “Who
thinks they know another measure in the diagram? Be ready to explain your answer. Show me ONE other measure that you know, and
hold up your whiteboard when you are ready.”
Teacher can show answers from students that used notation
correctly. Reveal the measures of AFE.
3. Show
students the statement below.
Ask them how we might fill in the blank, and why their answer makes sense.
4. Move
point C to the horizontal line (you can do this in the Geogebra applet).
Leaving
the measurements showing, ask students to tell you what they “spy”. They can write on their whiteboards, “I spy
__________________.” Answers must be
defended. Make sure to have the list of
possible answers written on the whiteboard.
The choices are angle bisector, midpoint, isosceles triangle, parallel
lines, and right angles.
3. Move point B to F. Move point A down the vertical line so your diagram looks like the one below.
Leaving the
measurements showing, ask student to tell you what they “spy”. They can write on their whiteboards, “I spy
__________________.” Answers must be
defended.
I SPY CHOICES: angle bisector, midpoint, isosceles triangle, parallel lines, and right angles.
4. Turn the
measurements off. Move point A back up
to the horizontal line, and make sure point B is on point F. Ask student to tell you what they “spy”. They can write on their whiteboards, “I spy
__________________.” Answers must be
defended.
I SPY CHOICES: angle bisector, midpoint, isosceles triangle, parallel lines, and right angles.
Extension
if there is time: Since we haven’t seen
parallel lines yet in this dynamic diagram, ask students how we can modify the diagram to form parallel
lines (and explain why).
There is a second page in the Geogebra Book that has a triangle rotated around a vertex by 180 degrees to form the second triangle. The hope is that this type of introduction will get students used to some of the types of diagrams that they will see throughout the unit. They will also get a chance to practice some of the thinking that is needed before the book gets to triangle congruence proofs.
I Spy Part II will have the I Spy Class Activity with answer keys.
