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.

Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6

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.

Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6

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.

Tags

CCSS.HSG.CO.B.6

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

Tags

CCSS.HSG.CO.B.6

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

Tags

CCSS.8.G.A.3

What symbol do we use for congruence?

Tags

CCSS.8.G.A.2

 △TRY≅△LIE.

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

Select all true statements.

Tags

CCSS.HSG.CO.B.6

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)

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

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

• D

• A

• I

• K

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

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

Tags

CCSS.8.G.A.3