Question

3 fill in the blank 12 points
quadrilateral c has exactly one pair of opposite parallel sides.
what shape is quadrilateral c? trapezoid
what other property about quadrilateral c must be true? choose your answer...
consecutive angles of quadrilateral c are supplementary.
each angle of quadrilateral c is a right angle.
each angle of quadrilateral c is congruent.
the diagonals of quadrilateral c are congruent.
4 multiple choice 6 points
quadrilateral z has the following properties:

• four congruent sides
• diagonals are perpendicular
• diagonals bisect opposite angles
• no right angles

what shape must quadrilateral z be?
rectangle

Explanation:

Sub - Question 3 (Second Part)

A trapezoid is defined as a quadrilateral with exactly one pair of parallel sides. For a trapezoid, when the two parallel sides (bases) are considered, the consecutive angles between a leg and each base are supplementary (their sum is \(180^{\circ}\)). The statement "Each angle of Quadrilateral C is a right angle" is only true for right trapezoids, not all trapezoids. The statement "Each angle of Quadrilateral C is congruent" is not true for most trapezoids. The statement "The diagonals of Quadrilateral C are congruent" is only true for isosceles trapezoids, not all trapezoids. So the correct property is that consecutive angles of Quadrilateral C are supplementary.

• A rectangle has four right angles, but Quadrilateral Z has no right angles, so it can't be a rectangle.
• A rhombus has four congruent sides, diagonals that are perpendicular, and diagonals that bisect opposite angles. Since Quadrilateral Z has four congruent sides, diagonals are perpendicular, diagonals bisect opposite angles, and no right angles, it matches the properties of a rhombus. (Note: The options are not fully shown, but based on the given incorrect option "Rectangle" and the properties, the correct shape should be a rhombus. If we assume the options include rhombus, the answer would be the option with "Rhombus".)

Answer:

Consecutive angles of Quadrilateral C are supplementary.

Sub - Question 4