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Determining Congruence

Determining Congruence 1.3 - Solution

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Starting with the two quadrilaterals, we see that they have the same shape, size, and orientation. What separates them is their position on the coordinate plane. By translating by units to the right and units down, we can map onto Therefore, they are congruent.

Regarding and they seem to have the same shape and size. However, since they have both different orientation and location, we are likely dealing with a rotation about the origin. Let's rotate about the origin

As we can see, a rotation about the origin maps onto Therefore, they are congruent. Regarding the final two triangles we see that they do not have the same shape. This means they can't be congruent.