Warm Up Write one net rule for the following composition of motion:

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Presentation transcript:

Warm Up Write one net rule for the following composition of motion: A translation three units right and two units down followed by a reflection across the line y=x Quadrilateral ABCD has an area of 4.5u2. If ABCD is dilated by a scale factor of 2.5, what is the area of A’B’C’D’? 10 minutes End

Answers Write one net rule for the following composition of motion: A translation three units right and two units down followed by a reflection across the line y=x Quadrilateral ABCD has an area of 4.5u2. If ABCD is dilated by a scale factor of 2.5, what is the area of A’B’C’D’? (y-2, x+3) 28.125 u2

Congruency

What do translations, reflections, and rotations have in common? Hint: Dilations do not have this property.

Congruent When the preimage and image have the same size and shape, we call the transformation an isometry, or a rigid motion. Definition: Two plane figures (polygons) are congruent if and only if one can be obtained from the other by a sequence of rigid motions.

Let’s Take a Look….. The definition of congruence tells you that when two figures are known to be congruent, there must be some sequence of rigid motion that maps one to the other. You will investigate this idea in the next example. Resource Manager: Grab a worksheet for each person. Time Keeper: 10 minutes Reader/Recorder: Read each question out loud, keep the group together. Spy Monitor: Check with other groups first, or the teacher key This first example has students find a sequence of rigid motion

Group Coordinates A(5, 1) B(3, 6) C(-2, 3) A(-4, -2) B(1, -5) C(0, 3)

Group Passing Game In your groups, plot your assigned coordinates on the poster paper. PASS! Write down a series of rigid motions (2 motions) Use the series of rigid motions to create the congruent triangle RST.

Homework Congruence Practice