Given two triangles, one with vertices 𝐴, 𝐵, and 𝐶, and the other with vertices 𝑋, 𝑌, and 𝑍, there are six different correspondences of the first with the second.

One such correspondence is the following:

A -> Z

B -> X

C -> Y

Write the other five correspondences.

Modified from EngageNY ©Great Minds Disclaimer

If all six of these correspondences come from congruences, then what can you say about ?

If two of the correspondences come from congruences, but the others do not, then what can you say about △𝐴𝐵𝐶?

Why can there be no two triangles where three of the correspondences come from congruences, but the others do not?

Give an example of two triangles and a correspondence between them such that (a) all three corresponding angles are congruent, but (b) corresponding sides are not congruent.

Draw your picture on paper, take a picture, and upload it using the image upload icon:

If you do not have the ability to upload an image of your work type "Picture is on paper."

Modified from EngageNY ©Great Minds Disclaimer

Give an example of two triangles and a correspondence between their vertices such that (a) one angle in the first is congruent to the corresponding angle in the second, and (b) two sides of the first are congruent to the corresponding sides of the second, but (c) the triangles themselves are not congruent.

Draw your picture on paper, take a picture, and upload it using the image upload icon:

If you do not have the ability to upload an image of your work type "Picture is on paper."

Modified from EngageNY ©Great Minds Disclaimer

Give an example of two quadrilaterals and a correspondence between their vertices such that (a) all four corresponding angles are congruent, and (b) two sides of the first are congruent to two sides of the second, but (c) the two quadrilaterals are not congruent.

Draw your picture on paper, take a picture, and upload it using the image upload icon:

If you do not have the ability to upload an image of your work type "Picture is on paper."

Modified from EngageNY ©Great Minds Disclaimer

A particular rigid motion, 𝑀, takes point 𝑃 as input and gives point 𝑃′ as output. That is, 𝑀(𝑃) = 𝑃′. The same rigid motion maps point 𝑄 to point 𝑄′. Since rigid motions preserve distance, is it reasonable to state that 𝑃𝑃′ = 𝑄𝑄′? Does it matter which type of rigid motion 𝑀 is? Justify your response for each of the three types of rigid motion. Be specific. If it is indeed the case, for some class of transformations, that 𝑃𝑃′ = 𝑄𝑄′ is true for all 𝑃 and 𝑄, explain why. If not, offer a counterexample.

Modified from EngageNY ©Great Minds Disclaimer