Vertices Line Segments Angles Warm-Up Using the picture of the two quadrilaterals (ABCD and PQRS) below and the cut-out of quadrilateral PQRS, determine the matching vertices, line segments, and angles from ABCD to PQRS: Describe the exact transformations (reflection, rotation, translation, etc.) that will move ABCD onto PQRS: How could you rename quadrilateral PQRS so that the name shows how its vertices correspond to those of quadrilateral ABCD? __________________

Opening Questions: What is the basic design element of these kaleidoscope designs? How were these designs created? Two figures that have the same size and shape are congruent. If you can flip, turn, and/or slide one figure exactly onto the other, the figures must be congruent.

Opening Questions: How are triangles used in the real world? Congruent triangles are used in many construction projects to provide strength and stability for structures. Now, let’s focus on triangles… George Washington Bride that connects New Jersey and New York City.

Problem Worksheet: Each group will get cut-out triangles, a ruler, a protractor, and a worksheet. List: Congruent line segments Congruent angles Corresponding vertices A sequence of transformations that move one triangle to another If the triangles are NOT congruent, describe why.

List all congruent line segments and angles: List all corresponding vertices: Describe a sequence of transformations that would move one triangle onto another. Are they congruent? Why or why not? Problem A:

List all congruent line segments and angles: List all corresponding vertices: Describe a sequence of transformations that would move one triangle onto another. Are they congruent? Why or why not? Problem B:

List all congruent line segments and angles: List all corresponding vertices: Describe a sequence of transformations that would move one triangle onto another. Are they congruent? Why or why not? Problem C:

List all congruent line segments and angles: List all corresponding vertices: Describe a sequence of transformations that would move one triangle onto another. Are they congruent? Why or why not? Problem D:

List all congruent line segments and angles: List all corresponding vertices: Describe a sequence of transformations that would move one triangle onto another. Are they congruent? Why or why not? Problem E:

List all congruent line segments and angles: List all corresponding vertices: Describe a sequence of transformations that would move one triangle onto another. Are they congruent? Why or why not? Problem F:

Is it always necessary to move one triangle onto the other to determine if they are congruent? No! If you know that the corresponding sides and angles are equal, you can conclude that the triangles are congruent. Can you conclude that two triangles are congruent if you know the measures of only one, two, or three pairs of corresponding parts?

You will need a whiteboard. On the board, I will show you a condition. For each case, give an argument to support your answer. If the conditions are not enough to determine two triangles are congruent, give a counterexample. Activity

Conditions: A.Can you be sure that two triangles are congruent if you know: 1. one pair of congruent corresponding sides? 2. one pair of congruent corresponding angles? B. Can you be sure that two triangles are congruent if you know: 1. two pairs of congruent corresponding sides? 2. two pairs of congruent corresponding angles? 3. one pair of congruent corresponding sides and one pair of corresponding angles?

Conditions: C. Can you be sure that two triangles are congruent if you know: 1. two pairs of congruent corresponding angles and one pair of congruent corresponding sides as shown? Use your understanding of transformations to justify your answer. 2. two pairs of congruent corresponding sides and one pair of congruent corresponding angles as shown? Use your understanding of transformations to justify your answer.

Conditions: D. Amy and Becky have different ideas about how to decide whether the conditions in the next part are enough to show triangles are congruent. 1. Amy flips GHI as shown. She says you can translate the triangle so that H corresponds to K and G corresponds to J. So all the measures in triangle GHI match measures in triangle JKL. Do you agree with Amy’s reasoning?

Conditions: