Question

If quadrilateral PQRS is a kite, which statements must be true? Check all that apply.

- QP ≅ QR
- PM ≅ MR
- QR ≅ RS
- ∠PQR ≅ ∠PSR
- ∠QPS ≅ ∠QRS

Answer 1

A kite is a quadrilateral in which two disjoint pairs of consecutive sides are congruent (“disjoint pairs” means that one side can’t be used in both pairs).

Then:

• 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.

Answer: correct options are A, B and E.

Answer 2

A, B, and E are the correct options.

A quadrilateral PQRS is a kite. Following are the key points related to the kites are as follow:

• Kites always are made up such that their adjacent sides are always congruent.

• Kites have two diagonals one is bigger and another one is smaller diagonal.

• Both diagonals are perpendicular to each other, and the intersection points are always the median to each of the diagonal.

Now, five different conditions are given in the question, based on these key points let us check which condition suited to the actual fact.

The following are the option wise explanation:

• Two disjoint pairs of consecutive sides are congruent by definition. Hence, QP≅QR.

• From the above statement, we can easily conclude that PM ≅ MR.

• QR ≅ RS, this is not true, since QR and RS are not adjacent sides.

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

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

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

To know more about quadrilaterals, please refer to the link:

https://brainly.com/question/13805601