Free math worksheets

- Check the square against each category one at a time. - A shape can belong to a smaller category and a larger category at the same time.

1. The shape is a square. 2. Its \(4\) square corners make it a rectangle. 3. Its \(4\) equal sides make it a rhombus. 4. Its \(4\) sides make it a quadrilateral. 5. It belongs in all four categories.

It should receive all four cards: square, rectangle, rhombus, and quadrilateral.

- Keep the category named in the problem. - Ask which larger category contains every rectangle. - Do not add a category that the “not a square” clue rules out.

1. The shape must receive the rectangle card. 2. Every rectangle has \(4\) sides, so it must also receive the quadrilateral card. 3. A rectangle that is not a square does not have to have \(4\) equal sides, so the rhombus card is not required. 4. The square card does not fit because the shape is stated not to be a square.

The cards that must fit are rectangle and quadrilateral.

- Keep the name already given. - Ask which larger category contains every rhombus. - Use the corner clue to rule out two categories.

1. The shape is a rhombus because it has \(4\) equal sides. 2. It is also a quadrilateral because it has \(4\) sides. 3. It is not a rectangle or square because it does not have \(4\) square corners.

The names that fit are rhombus and quadrilateral.

- Test the first claim with a rectangle that has two different side lengths. - Test the second claim with the most special rectangle. - Use one counterexample for each statement.

1. A rectangle that is not a square does not have all \(4\) sides equal, so it is not a rhombus. This disproves Mia's statement. 2. A square has \(4\) square corners, so it is a rectangle, and \(4\) equal sides, so it is a rhombus. 3. The square disproves Leo's statement. 4. Some rectangles are rhombuses, and some are not.

Both are wrong. A non-square rectangle is not a rhombus, but a square is both a rectangle and a rhombus.

- Compare the required corner attributes first. - Then find a side-length feature that some rectangles have but squares do not. - Use one example type to show why the reverse statement fails.

1. Every square has \(4\) square corners, so every square meets the rectangle rule. 2. A rectangle can have two different side lengths. 3. A rectangle with two different side lengths does not have \(4\) equal sides, so it is not a square. 4. Therefore, all squares are rectangles, but some rectangles are not squares.

Squares have the \(4\) square corners required for rectangles. Some rectangles have two different side lengths, so they are not squares.

- Test whether every rectangle must have the side attribute of a rhombus. - Test whether every rhombus must have the corner attribute of a rectangle. - Use the square to identify where the two categories overlap.

1. A rectangle that is not a square does not have all \(4\) sides equal, so it is not a rhombus. 2. A rhombus that is not a square does not have all \(4\) square corners, so it is not a rectangle. 3. A square has both attributes, so it belongs to both categories. 4. Therefore, neither category contains all of the other; the categories overlap at squares.

No. Some rectangles are not rhombuses, and some rhombuses are not rectangles. Squares belong to both categories.