Question

question 8
6.67 pts
if pqrs is a rhombus, which statement must be true?
diagram of rhombus pqrs with diagonals
options:

• ∠pqr ≅ ∠qrs
• pq ≅ qr
• ∠psr is a right angle
• pr ≅ qs

question 9
6.67 pts
which of the following quadrilaterals always have diagonals that are congruent? check all that apply

• squares
• rectangles
• trapezoid
• parallelogram
• rhombus

Explanation:

Step1: Recall rhombus properties

A rhombus has all sides congruent, so \(PQ = QR = RS = SP\).

Step2: Evaluate each option

• \(\angle PQR \cong \angle QRS\): Adjacent angles in a rhombus are supplementary, not necessarily congruent.
• \(PQ \cong QR\): True (all sides of a rhombus are congruent).
• \(\angle PSR\) is a right angle: Only true if the rhombus is a square, not always.
• \(PR \cong QS\): Diagonals of a rhombus are not congruent unless it is a square.

Step3: Recall quadrilateral diagonal properties

• Squares: Diagonals are congruent.
• Rectangles: Diagonals are congruent.
• Trapezoid: Only isosceles trapezoids have congruent diagonals, not all trapezoids.
• Parallelogram: Diagonals are not congruent unless it is a rectangle/square.
• Rhombus: Diagonals are not congruent unless it is a square.

Answer:

Question 8: \(PQ \cong QR\)
Question 9: Squares, Rectangles