My daughter is in 3rd grade and starting some basic geometry. Her homework today shows a parallelogram with the 4 corners labeled LMNO. Her first question is give two names for this parallelogram. Her answers were LM and NO. I told her that those were two of the sides, but that the parallelogram as a whole must be labeled with all four corners, so two names could be LMNO or NOLM. She says that I'm wrong...am I? She forgot her math book at school, so I cannot check there. She was also asked to name the 2 triangles formed after she drew the diagonal LN. She wrote LN and NL. I told her that was the name of the diagonal, but that the triangles would be LNO and LMN. She again says that I am wrong. It has been awhile since I've done this stuff, but I can't be that far off. Please let me know what you think!

LM and NO describe lines between two points. A parallelogram requires 4 points, and a triangle requires 3.

You are correct in your explanations. Let me break it down for you and your daughter.

For the first question, your daughter was asked to give two names for the parallelogram with corners labeled LMNO. A parallelogram is a quadrilateral with opposite sides parallel. In this case, the opposite sides are LM and NO. However, when naming a shape, we typically refer to all its corners. So, the correct names for this parallelogram would be LMNO and NOLM, as you mentioned.

Now, let's move on to the second question about naming the two triangles formed by the diagonal LN. When a diagonal is drawn inside a quadrilateral, it splits it into two triangles. In this case, the diagonal LN divides the parallelogram into two triangles: LNO and LMN. It's important to note that the order of the vertices determines the name of the triangle. Therefore, your answer of LNO and LMN is correct, while LN and NL only refer to the diagonal itself.

It's great that you're helping your daughter with her geometry homework. Remember, always double-check the instructions and definitions of geometric shapes to ensure accurate naming.