Sequence of Transformations to Prove Congruency

Triangle ABC is congruent to triangle EDF. So, Kiran knows that there is a sequence of rigid motions that takes ABC to EDF. Select all true statements after the transformations:

• Angle A coincides with angle F

• Angle B coincides with angle D.

• Segment AC coincides with segment EF.

• Segment BC coincides with segment ED.

• Segment AB coincides with segment ED.

Determine if the two figures are congruent by using transformation. If so, what kind of transformation?

• congruent; a counterclockwise rotation of 90 degrees followed by a translation

• congruent; reflection

• congruent; translation

• not congruent

Which conclusions can be made? Select all that apply!

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Which of the following are congruence transformations? (select all that apply)

• Translations

• Dilations

• Rotations

• Reflections

• Reflection across the x-axis, translation down 4 and right 1.

• Rotation 180° about the origin, translation down 1 and right 2.

• Rotation 180° about the origin, translation down 2 and right 2.

• Reflection across the x-axis, down 6 and right 3.

#1

Which of the following create congruent images? Select all that apply.

• Translations

• Reflections

• Rotations

• Dilation

Choose the congruency transformation that proves the two pentagons to be congruent.

• 180 rotation followed by translation 1 to the right

• X-axis reflecton followed by y-axis reflection

• Reflection across line y=x followed by translation 1 to the right

• Y-axis reflection followed by 180 rotation

The figures below are congruent. Which series of transformations maps figure ABCD onto EFGH?

• rotation followed by a translation

• rotation followed by a dilation

• reflection followed by a translation

• reflection followed by a rotation

In order to prove that two figures are congruent, I must show that I can map one to the other using the following transformations (select all that apply):

• Translation

• Rotation

• Reflection

• Dilation

Answer explanation

Congruent figures have the same shape AND size. This means all side lengths are equal. If a dilation is applied, that means the image and preimage are not the same size and therefore not congruent.