Proving Congruent Figures using Rigid Motions

In the figure below, △ ABC ≅△ A'B'C'. Which transformation maps △ ABC onto △ A'B'C'?

• Reflect △ ABC in the x-axis.

• Translate △ ABC 3 units left and 6 units down.

• Reflect △ ABC in the y-axis, then rotate it 90° counterclockwise about the origin.

• Rotate △ ABC 180° counterclockwise about the origin.

Which best explains whether or not ΔABC ≅ ΔLMN?

• The figures are congruent because a 270° rotation about the origin and then a reflection over the x-axis will map ΔABC onto ΔLMN.

• The figures are congruent because a 180 rotation about the origin and then a reflection over the x-axis will map ΔABC onto ΔLMN.

• The figures are not congruent because point B corresponds with point N and point C corresponds with point M.

• The figures are not congruent because there is no rigid transformation or combination of rigid transformations that will map ΔABC onto ΔLMN.

Use rigid motions to explain why ∆ABC ≅ ∆XZY. #42

• If ∆ABC is rotated around the origin 180 degrees, it will map to ∆XYZ. Since Rotations preserve shape and size, the triangles are congruent.

• If ∆ABC is translated, it will map to ∆XYZ. Since Rotations preserve shape and size, the triangles are congruent.

• If ∆ABC is reflected across the y-axis, it will map to ∆XYZ. Since Rotations preserve shape and size, the triangles are congruent.

• If ∆ABC is rotated around the origin 90 degrees, it will map to ∆XYZ. Since Rotations preserve shape and size, the triangles are congruent.

Why do rigid motions create figures that are congruent?

• They change the shape

• They change the size

• They keep the shape and size the same

• they change the size and shape

What are the series of rigid motions that would map ∆ABC onto ∆A''B''C''?

• a reflection followed by a rotation

• a reflection followed by a translation

• a translation followed by a rotation

• a translation followed by a reflection

What symbol do we use for congruence?

 △TRY≅△LIE.

So, there is a sequence of rigid motions that takes TRY to LIE.

Select all true statements.

If Triangle ABC translated 4 units to the right, where would the new location of point B' be located?

• (1, 0)

• (3, 0)

• (4, 0)

• (0, 1)

Triangle ABC reflected across the y-axis to become Triangle IDK. Which point corresponds (same position as) Point C?

• D

• A

• I

• K

Which could describe the transformation shown?

• Reflect across the y-axis, then translate down 1 and right 1

• Reflect across the y-axis

• Translate down 1 and right 1

• Reflect across the x-axis, then translate down 1 and right 1