IXL - Prove triangles are congruent using rigid motions (Geometry practice)

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congruent to

△

Justify your answer using rigid motions.

Yes. A translation can map

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onto

△

Yes. A reflection can map

△

onto

△

No. It is not possible to map

△

onto

△

using only rigid motions.

ref_doc_title.

Learn with an example

question

△

congruent to

△

Justify your answer using rigid motions.

Yes. A translation and a reflection can map

△

onto

△

Yes. A translation and a rotation can map

△

onto

△

No. It is not possible to map

△

onto

△

using only rigid motions.

key idea

Two figures are congruent if and only if one can be mapped onto the other using rigid motions.

Rigid motions map line segments to congruent line segments and map angles to congruent angles. Reflections, rotations, and translations are rigid motions. Dilations are not.

So, two figures are congruent if and only if all pairs of corresponding sides and angles are congruent.

solution

Determine if the sides and angles of

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are congruent to their corresponding sides and angles in

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The corresponding sides are not all congruent. For example, there is no side in

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that is congruent to

So,

no,

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is not congruent to

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It is not possible to map

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onto

△

using only rigid motions.

Looking for more? Try these:

Lesson: Transformations

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Teacher tools

Work it out

Not feeling ready yet? These can help:

K.3Identify congruent figures

H.1Classify congruence transformations

Lesson: Transformations

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