Question

classify each statement as true or false.

1. every parallelogram is a quadrilateral.

14 every quadrilateral is a parallelogram.

1. all angles of a parallelogram are congruent.
2. all sides of a parallelogram are congruent.
3. in ▶rstu, (overline{rs}paralleloverline{tu}).
4. in ▶abcd, if (mangle a = 50^{circ}), then (mangle c = 130^{circ}).
5. in ▶xwyz, (overline{xy}congoverline{wz}).
6. in ▶abcd, (overline{ac}) and (overline{bd}) bisect each other.

Explanation:

• 13: A parallelogram has four sides, so it is a quadrilateral.
• 14: A quadrilateral (e.g., trapezoid) may not have both pairs of opposite sides parallel (a property of parallelograms).
• 15: In a parallelogram, opposite angles are congruent, but not all angles are necessarily congruent (except in special cases like a rectangle).
• 16: In a parallelogram, opposite sides are congruent, not all sides (except in special cases like a rhombus).
• 17: By the definition of a parallelogram, opposite sides are parallel. In parallelogram \(RSTU\), \(\overline{RS}\) and \(\overline{TU}\) are opposite sides.
• 18: In a parallelogram \(ABCD\), \(\angle A\) and \(\angle C\) are opposite angles. Opposite angles of a parallelogram are congruent, so \(m\angle C = 50^{\circ}\).
• 19: In a parallelogram \(XWYZ\), \(\overline{XY}\) and \(\overline{WZ}\) are opposite sides. Opposite sides of a parallelogram are congruent.
• 20: One of the properties of a parallelogram is that its diagonals bisect each other. In parallelogram \(ABCD\), \(\overline{AC}\) and \(\overline{BD}\) are diagonals.

Answer:

1. True
2. False
3. False
4. False
5. True
6. False
7. True
8. True