Question

analyzing diagrams of quadrilaterals
which statements are true regarding quadrilateral abcd? choose three correct answers.
abcd is not a parallelogram.
abcd is a rhombus.
abcd is not a rectangle.

Explanation:

Step1: Recall the properties of parallelograms

A parallelogram has opposite sides equal. In the given quadrilateral \(ABCD\), \(AB = AD\) and \(BC = CD\) (marked with equal - side marks). Also, one angle (\(\angle C\)) is a right angle.

Step2: Recall the properties of rhombus

A rhombus has all sides equal. Here, from the side - marking, we can assume all sides are equal (since \(AB = AD\) and \(BC = CD\) and if \(AB = BC\) which is likely from the diagram's side - marking convention).

Step3: Recall the properties of rectangle

A rectangle has four right angles. Since only \(\angle C\) is shown as a right angle (and we have no information about other angles being right angles), it is not a rectangle. Also, a parallelogram has opposite sides parallel and equal. A rhombus is a special type of parallelogram with all sides equal. But if we consider the fact that for a rectangle all angles must be \(90^{\circ}\), and here only one angle is \(90^{\circ}\) (assuming from the diagram), \(ABCD\) is not a rectangle. And a rhombus (a type of parallelogram with all sides equal) can have one right angle (in fact, if a rhombus has one right angle, it is a square, but a square is also a rhombus).

Answer:

ABCD is a rhombus, ABCD is not a rectangle.