1 multiple choice 1 point a parallelogram must be a rectangle if its diagonals bisect the angles through which they pass are congruent are perpendicular to each other bisect each other 2 multiple choice 1 point given the rhombus pqrs with diagonals $ \overline { p r } $ and $ \overline { q s } $. which of the following is not necessarily true? $ \angle p s q \cong \angle p r q $ $ \overline { p r } \perp \overline { q s } $ $ \overline { p r } $ bisects $ \angle q p s $ and $ \angle q r s $ $ \angle p s q \cong \angle s q r $ 3 multiple choice 1 point how are a rhombus and a square alike? they both have four equal sides. they both have four equal angles. they both have only one pair of parallel sides. they both have four right angles.

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Accepted Answer

# 1.
## Brief Explanations:
- **Option 1**: Diagonals bisecting angles is a property of a rhombus, not a rectangle.
- **Option 2**: In a parallelogram, if diagonals are congruent, it is a rectangle (by the rectangle - parallelogram congruent diagonals theorem).
- **Option 3**: Diagonals perpendicular to each other is a property of a rhombus.
- **Option 4**: Diagonals bisecting each other is a property of all parallelograms.

# Answer:
B. are congruent

# 2.
## Brief Explanations:
- **Option 1**: In a rhombus $PQRS$ with diagonals $PR$ and $QS$, $\angle PSQ$ and $\angle PRQ$ are not necessarily congruent.
- **Option 2**: The diagonals of a rhombus are perpendicular ($PR\perp QS$).
- **Option 3**: The diagonals of a rhombus bisect the vertex angles ($PR$ bisects $\angle QPS$ and $\angle QRS$).
- **Option 4**:  In a rhombus, adjacent angles formed by a diagonal and a side are congruent ($\angle PSQ\cong\angle SQR$ because $PS\parallel QR$ and $QS$ is a transversal, and also using the properties of a rhombus).

# Answer:
A. $\angle PSQ\cong\angle PRQ$

# 3.
## Brief Explanations:
- **Option 1**: A rhombus has four equal - length sides, and a square (which is a special type of rhombus) also has four equal - length sides.
- **Option 2**: A rhombus has opposite angles equal, but not all angles are equal (unless it is a square). A square has four equal angles (all $90^{\circ}$).
- **Option 3**: Both a rhombus and a square have two pairs of parallel sides.
- **Option 4**: A rhombus does not have four right angles (unless it is a square). A square has four right angles.

# Answer:
A. They both have four equal sides.

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