Proving Figures are Congruent Using Rigid Motions

Proving Figures are Congruent Using Rigid Motions

I can prove two shapes are congruent using rigid motions.

The big idea

• Congruent figures have the same side lengths and angle measures. They will appear to be the same size and the same shape.

• If I can carry one figure onto another using rotations, reflections, or translations the figures are congruent.

• If figures are congruent there are rigid transformations that will carry one figure onto the other.

Multiple Choice

How would you carry ABCD onto EFGH?

• Translate left 3 units and up 4 units

• A reflection across the line y=x

• Translate right 3 units and down 4 units

• A rotation 180 degrees

Multiple Choice

Are ABCD and EFGH congruent?

• Yes

• No

Multiple Choice

Observe JKLM and NPQR. Describe the transformation.

• NPQR is a translation 3 units down and 2 units right from JKLM.

• NPQR is a reflection of JKLM

• NPQR is a translation 5 units down and 5 units right from JKLM.

• There are not possible transformations

Multiple Choice

JKLM and NPQR___ congruent because there ______ a rigid motion that maps one to the other.

• are, is not

• are, is

• are not, is not

• are not, is

Multiple Select

Select the correct answers.

• There is not a sequence of rigid motions that maps triangle LMN to triangle DEF.

• There is a sequence of rigid motions that maps triangle LMN to triangle DEF.

• The two figures are congruent.

• The two figures are not congruent.

Open Ended

How do the sizes of the pairs of figures help determine if they are congruent?

Multiple Choice

Use the definition of congruence to decide whether the two figures are congruent. Explain your answer.

The two figures appear to be ______ size and ______ shape.

• the same, the same

• a different, a different

• a different, the same

• the same, a different

Multiple Choice

Use the definition of congruence to decide whether the two figures are congruent. Explain your answer.

Which of the following will map triangle FGH (blue) onto triangle F'G'H' (green)?

• a clockwise rotation of 90 degrees about the origin

• a counter-clockwise rotation of 90 degrees about the origin

• a reflection across the x-axis

• a reflection across the y-axis

Multiple Choice

Use the definition of congruence to decide whether the two figures are congruent. Explain your answer.

A rotation ___ a rigid motion so triangles FGH and F'G'H ___ congruent.

• is, are

• is, are not

• is not, are

• is not, are not

Multiple Choice

Use the definition of congruence to decide whether the two figures are congruent. Explain your answer.

The two figures appear to be ______ size and ______ shape.

• the same, the same

• a different, a different

• a different, the same

• the same, a different

Multiple Select

Which rigid motion(s) would correctly map MPT onto ZYX?

• a reflection across the x-axis

• a reflection across the y-axis

• a translation

• a rotation

Open Ended

Can figures have congrent angles but not be congruent figures? Explain.

Poll

How do you feel about proving two shapes are congruent using rigid motions?

• I understand this and feel confident I can get it correct on a test.

• I am understanding this, but I could still use some additional practice.

• I can do part of this, but there are parts that I need help with.

• I need to come to tutoring because I have no idea what to do.

Poll

Which activity do you prefer during synchronous time?

• quizizz

• pear deck

• a mix of both

• I do not like either