Question

which statements are true regarding quadrilateral abcd? check all that apply. abcd has congruent diagonals. abcd is a rhombus. abcd is not a rectangle. abcd is not a parallelogram. abcd has four congruent angles.

Explanation:

Step1: Recall properties of quadrilaterals

A rhombus has all - sides equal. In the given quadrilateral ABCD, the equal - side markings indicate that all four sides are equal, so it is a rhombus.

Step2: Recall rectangle properties

A rectangle has four right - angles. Since there is only one right - angle marked and not all four, ABCD is not a rectangle.

Step3: Recall parallelogram properties

A rhombus is a special type of parallelogram, so the statement that ABCD is not a parallelogram is false.

Step4: Recall congruent - diagonal properties

In a rhombus, the diagonals are perpendicular bisectors of each other but not congruent (except in the case of a square which is a special rhombus). Here, there is no indication that it is a square, so the diagonals are not congruent.

Step5: Recall congruent - angle properties

A rhombus does not have four congruent angles (except when it is a square). Since there is only one right - angle marked, the angles are not all congruent.

Answer:

ABCD is a rhombus.
ABCD is not a rectangle.