Triangle FIX is congruent to triangle TOP. Name three pairs of corresponding vertices. Name three pairs or corresponding sides. Name three pairs of corresponding angles. Is it correct to say that...

Triangle FIX is congruent to triangle TOP.

Name three pairs of corresponding vertices.

Name three pairs or corresponding sides.

Name three pairs of corresponding angles.

Is it correct to say that triangle POT is congruent to triangle XIF? Why or why not?

Is it correct to say that triangle IFX is congruent to triangle PTO? Why or why not?

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Borys Shumyatskiy | College Teacher | (Level 3) Associate Educator

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Hello!

When it is said that two triangles are congruent, the order in which the vertices are listed is important.

In our case, the corresponding vertices are F and T, I and O, X and P.

This means that the angles at these vertices are equal, i.e.

`/_` XFI = `/_` PTO, `/_` FIX = `/_` TOP, `/_` IXF = `/_` OPT.

And the corresponding sides are equal, namely

FI = TO, IX = OP, XF = PT.

The same triangle may be named in the different order of vertices. If the vertices of the congruent triangle are reordered the same way, the correspondence of vertices will remain and two "new" triangles will be also congruent. If not, the "renamed" triangles may occur not to be equal.

Actually, it is important that the same sides and angles be equal.

Now for your question, "Is it correct to say that triangle POT is congruent to triangle XIF?" We have to check whether the correspondence is preserved. It is sufficient to check the correspondence of vertices.

The pairs now are P and X, O and I, T and F. These pairs are the same as at the beginning. The answer is YES, these renamed (and interchanged) triangles are congruent.

For the second variant of rearragement, "Is it correct to say that triangle IFX is congruent to triangle PTO?", the answer is NO. The pairs of corresponding vertices are I and P, F and T, X and O. The only preserved pair is F and T, but two other are different.

(X corresponds to O for congruent triangles means that the angles at these vertices are the same, but it isn't given and may be false)

Hope this helps.

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