• SAT
High School

If quadrilateral PQRS is a kite, which statements must be true? Select three options.

A. \( QP \cong QR \)
B. \( PM \cong MR \)
C. \( QR \cong RS \)
D. \( \angle PQR \cong \angle PSR \)
E. \( \angle QPS \cong \angle QRS \)

Answer :

If quadrilateral pqrs is a kite, the statements that must be true is that:

  • qp ≅ qr
  • pm ≅ mr
  • ∠qps ≅ ∠qrs.

What are quadrilateral?

This is a term that is found in geometry. A quadrilateral is known to be a kind of a closed, two-fold shape that has four straight sides.

The polygon is also known to have four vertices or corners. The shape of quadrilaterals can be seen in a lot of things around us. If quadrilateral pqrs is a kite, the statements that best shows that it is a kite are qp ≅ qr, pm ≅ mr , and ∠qps ≅ ∠qrs.

Learn more about quadrilateral from

https://brainly.com/question/23935806

Answer:

A, B, and E are the correct options.

Explanation:

Two disjoint pairs of consecutive sides are congruent by definition - QP≅QR and QR is not congruent to RS (one side can’t be used in both pairs);

One diagonal (segment QS, the main diagonal) is the perpendicular bisector of the other diagonal (segment PR, the cross diagonal), so PM≅MR;

The opposite angles at the endpoints of the cross diagonal are congruent, thus ∠QPS≅∠QRS.

∠PQR is not congruent to ∠PSR, because they are not angles at the endpoints of the cross diagonal.

Therefore, A, B, and E are the correct options.

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