ABCD is a rhombus. Explain why...

Question

anonymous · Answer

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mathstudent55 · Answer

The info you give, the two congruent triangles, is not enough to prove ABCD is a rhombus. It's enough to prove it's a parallelogram.

mathstudent55 · Answer

You mean the given info is that ABCD is a rhombus and you want to know why you know those 2 triangles are congruent?

anonymous · Answer

Yes, please.

mathstudent55 · Answer

Ok, since ABCD is a rhombus, opposite sides are congruent.

mathstudent55 · Answer

That means side AB is congr to side DC and side AD is congr to side BC.
All of that is from the definition of a rhombus which is also a parallelogram.

mathstudent55 · Answer

Side AC is congruent to itself.

mathstudent55 · Answer

So you have three sides of one triangle, ABC which are congruent to three sides of another triangle, so the triangles are congruent by SSS.

anonymous · Answer

Oh okay, this makes sense. Thank you for for helping me with this!