# Triangle congruence (lesson)

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Overview
Students explore the congruence postulates. They recognize which constraints are insufficient to guarantee congruence. This is a introductory activity to lead into proving two triangles are congruent.

Main Standard
5.0 Students prove that triangles are congruent or similar, and they are able to use the concept of corresponding parts of congruent triangles.

Materials
1 copy of Triangle Congruence Cards (on cardstock, pre-cut)
1 Protractor per student
1 Ruler per student
Half sheets of transparencies (1 per group)
Half sheets of scratch paper
Triangle Congruence Questions Sheet
Triangle Congruence Cards (1 transparency or enough for class)

Activity Notes
Divide the class into 8 teams. Give each team half of an overhead sheet of paper, each student a ruler and a protractor. Instruct the teams to draw a triangle of any kind on the overhead, not too small and making it interesting (i.e. you donâ€™t want s bunch of equilateral triangles or right triangles, you want a mixture)

Have students measure the sides and angles of the triangle and label their triangle with the appropriate measurement.

Playing the Game
A team is selected to send a representative to display their triangle on the overhead.
A team then selects a challenge card from cards – they can be all face up.
The team representative then marks the appropriate side/angles on their triangle to match the challenge card.
The team representative returns to the team.
The entire class is given 3 minutes to draw as many different triangles they can that are NOT congruent to the initial triangle but the side/angles chosen from the challenge card MUST be congruent to the team triangle.

Note: The triangles must be obviously different than the original

After 3 minutes, call time. Give each person in the group the opportunity to compare their triangles and mark those that are actually different.

After 30 seconds, survey the class to see which group got the most different triangles.
You can check if the triangles created are indeed different but satisfying the given properties by overlaying the transparency on the triangles.

Scoring the Game
If the team who gets the most different triangles than the original triangle, they get a point for each different triangle.
If the winning team is the host team, then they get double the points.
Any invalid triangle is minus one point.
If there could be NO triangle drawn that is different to the original triangle, then the host team gets 5 points.

Analysis
As you go though the cards, start a chart on the wall that includes the conditions in which a different triangle could be drawn and one that could not be drawn. This chart will be the building block for discussing the properties of congruent triangles.

As you come across triangles that are forced to be congruent, discuss why this occurs.

Homework
End the game 5 minutes early. Have the teams copy the triangles down from the teams that have not been done and give them conditions associated with each triangle. Students are to draw three triangles with the given conditions if possible. If it is not possible to generate the triangles, then the students have state the reason why it is not possible.

The Next Day
Continue your chart and discuss what is needed to ensure triangle congruence. Use the experience with this activity as a lead into to your discussion of now formally proving two triangles are congruent. Pass out the Triangle Congruence Questions Sheet. Place a copy of the triangle congruence cards on the overhead or pass out copies to the class. Have students answer the questions in teams and discuss the answers.

(see attachments for all lesson documents)