# Predicting Congruence

#### 1 Hook/Attention Getter

On a projector, show the students a picture of a right triangle with side lengths of 8 in. and 6 in. Show another right triangle with a side length of 6 in. and 10 in. Also, label both triangles with one 30 degree angle in corresponding places. Have students pair up and determine whether they think the two triangles are congruent and why. After a few minutes of discussion, bring the class together and discuss why the triangles were congruent and how they knew.

Given the two triangles, you are your partner need to investigate them and determine whether they are congruent or not. Be ready to share your answers and supporting evidence with the class.

#### 2 Guided Practice

Explain the directions of the worksheet found at http://misscalculate.blogspot.com/2015/04/triangle-congruence-proofs-par... Have students log onto Chrome books and find the Geogebra website where they will do their work.

Log onto Geogebra and split up the following triangles with your group members. Create your triangle on Geogebra, print the triangle, and label the triangle as they did in the example problem. When your group is finished, make predictions about each triangle. Will all the other groups have the exact same Triangle A as your group did? Why or why not?

#### 3 Independent Practice

After students print out their triangles and make their predictions, have them post all Triangle As in one side of the board, Triangle Bs on another part of the board and so on. Then, instruct students to grab their predictions and do an individual gallery walk to assess their predictions. They need to answer the questions:

1. Were their predictions correct? Why or why not?

2. If the triangles are congruent, what parameters made them all be the same?

You will be doing an individual gallery walk around all the groups of triangles. For each group of triangles, you need to answer the following questions. Be prepared to support your answer and share with your group.

1. Were their predictions correct? Why or why not?

2. If the triangles are congruent, what parameters made them all be the same?

#### 4 Group Discovery

Students will work together to try to classify the groups of triangles as SAS, ASA, HL, AAS, SSS. They will need to record all of their findings.

You and your teammates will compare notes and come up with rules for each type of congruent triangle group. Be ready to share your answers with the class.

#### 5 Wrap-Up

As a class, discuss their findings and fill out the tool kit with all of the Triangle Congruence Conjectures. Have students share their findings and add any information for them that they could not come up with on their own.

As the group discusses what they found, fill in the Triangle Toolkit so that you will be able to use this when proving other triangles congruent.