Question

12 multiple choice 1 point
if the diagonals of a parallelogram are perpendicular and not congruent, then the parallelogram is
a square
a rectangle
a rhombus
an isosceles trapezoid
13 multiple choice 1 point
if quadrilateral abcd is a parallelogram, which statement must be true?
$overline{ac}perpoverline{bd}$
$overline{ac}congoverline{bd}$
$overline{ac}$ and $overline{bd}$ bisect each other.
$overline{ac}$ bisects $angle dab$ and $angle bcd$.

Explanation:

12

Step1: Recall properties of parallelograms

• Square: Diagonals are perpendicular, congruent, and bisect each other.
• Rectangle: Diagonals are congruent and bisect each other.
• Rhombus: Diagonals are perpendicular and bisect each other (not congruent unless it's a square).
• Isosceles trapezoid: Not a parallelogram.

Since the diagonals are perpendicular and not congruent, it matches the properties of a rhombus.

13

Step1: Recall properties of parallelograms

• Property of diagonals in a parallelogram: The diagonals of a parallelogram bisect each other.
• For \( \overline{AC}\perp\overline{BD}\): This is true for rhombus (a special - case parallelogram), not for all parallelograms.
• For \( \overline{AC}\cong\overline{BD}\): This is true for rectangles (a special - case parallelogram), not for all parallelograms.
• For \( \overline{AC}\) bisects \( \angle DAB\) and \( \angle BCD\): This is true for rhombus (a special - case parallelogram), not for all parallelograms.

Answer:

1. C. a rhombus
2. \( \overline{AC}\) and \( \overline{BD}\) bisect each other.