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Special Parallelograms

Properties

For any rhombus JKLM, decide whether the statement ∠L≅∠M is always, never, or sometimes true. Explain your reasoning.

Properties

For any rhombus JKLM, decide whether the statement sides LM≅MJ is always, never, or sometimes true. Explain your reasoning.

Properties

For any rhombus JKLM, decide whether the statement diagonals LJ≅MK is always, never, or sometimes true. Explain your reasoning.

Given that ABDC is a rhombus, what are the measurements of angles 1 through 8? What are the total measures each for A, B, C, and D?

Real world

You're putting down tile in an oddly shaped room. The tile comes in 1 foot squares (1'x1') or rhombuses with each side measuring 1 foot and acute angles of 45 degrees. If the layout of the room is shown above with linear measurements in yards, how many of each type of tile are you going to need?