Questions

Decide whether each statement is always, sometimes, or never true. Explain your answer.

1. A square is a rectangle.

2. A rhombus is a square.

3. An isosceles trapezoid is a trapezoid.

4. A parallelogram is a quadrilateral.

5. A square is a parallelogram.

6. A trapezoid is a parallelogram.

Decide what type of quadrilateral it must be and what type of quadrilateral it could be based on the description.

7. A quadrilateral has 4 congruent angles.

8. A quadrilateral has 2 pairs of congruent sides.

9. Draw a kite. Draw in its diagonals. Make at least one conjecture about the diagonals of kites.

10. Draw a rectangle. Draw in its diagonals. Make at least one conjecture about the diagonals of rectangles.

11. Draw a rhombus. Draw in its diagonals. Make at least one conjecture about the diagonals of rhombuses.

12. Draw a kite. Make a conjecture about the opposite angles of kites.

Use the markings on the shapes below to identify the shape. Then, solve for \begin{align*}x\end{align*}Note: pictures are not drawn to scale.