ShmoopTube

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Here’s the unshmoopiest question that ever there was…

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The graph below shows a right triangle XYZ along with a segment AB. 

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Suppose a point C is to be plotted so that the newly formed triangle, ABC,

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would be congruent to triangle XYZ.

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What could be a possible coordinate for point C?

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And here are the potential answers...

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First we have to keep in mind what “congruence” means:

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All corresponding sides and angles must be the same.

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Note that our new triangle doesn’t have to be oriented the same way as the first one…

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…and trust us, they’re gonna try to get ya there.

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Note that, while the triangle up top has its 5-unit side on the bottom…

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…this second triangle has its 4-unit side on the bottom. So there’s going to be some spinnage here.

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Let’s take these one at a time…

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A wouldn’t work, because if we were to plot a point at 2,4…

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… we’d wind up with a side that has a length of 2…

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…which our original triangle did not have. Buh-bye.

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What about option B?

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Hullo! We’ve got a 3-4-5 triangle… just like the original.

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We think we’ve found our answer, but let’s make sure…

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C’s not gonna happen. Placing a point at 1,5 is going to give us an obtuse angle.

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So, unless we’re obtuse ourselves… we’re not gonna pick that one.

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And D is a no-go, because we get an isosceles triangle.

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So B it is.

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As in… “Booyah!”

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