Question

#9) look at the venn diagram. read each statement and write a, b, c, d, e, f, and g in the correct part of the venn diagram.rectanglerhombusa) two sets of parallel sidesb) four right anglesc) opposite angles are congruentd) all sides are congruente) two lines of symmetryf) diagonals bisect each other at right anglesg) four sides and four anglesread each statement and circle always, sometimes, or never for each statement shown.#10) a square is ____________ a parallelogram. always sometimes never#11) a trapezoid is __________ a rectangle. always sometimes never#12) a rhombus is __________ a quadrilateral. always sometimes never#13) a square is __________ a rhombus. always sometimes never#14) the sum of the angles of a quadrilateral is __________ degrees.#15) in parallelogram wxyz, the measure of angle w is 80 degrees. what is the measure of each angle?angle x = ______angle y =

Explanation:

Step1: Assign to Rectangle only

• B) Four right angles
• E) Two lines of symmetry

Step2: Assign to Rhombus only

• D) All sides are congruent
• F) Diagonals bisect each other at right angles

Step3: Assign to Overlap (both)

• A) Two sets of parallel sides
• C) Opposite angles are congruent
• G) Four sides and four angles

Step4: Solve #10: Square-parallelogram

A square has all parallelogram properties.

Step5: Solve #11: Trapezoid-rectangle

Trapezoids have only 1 parallel side pair.

Step6: Solve #12: Rhombus-quadrilateral

Rhombuses have 4 sides/angles by definition.

Step7: Solve #13: Square-rhombus

Squares have all rhombus properties.

Step8: Solve #14: Quadrilateral angle sum

Use quadrilateral angle sum formula: $(4-2)\times180^\circ$

Step9: Solve #15: Parallelogram angles

Opposite angles congruent, adjacent supplementary.
$\angle W = 80^\circ$, so $\angle Y = 80^\circ$; $\angle X = \angle Z = 180^\circ - 80^\circ = 100^\circ$

Answer:

#9 Venn Diagram Placement:

• RECTANGLE only (non-overlapping left circle): B, E
• RHOMBUS only (non-overlapping right circle): D, F
• Overlap (both shapes): A, C, G

#10: always

#11: never

#12: always

#13: always

#14: $360$

#15:

Angle X = $100^\circ$
Angle Y = $80^\circ$
Angle Z = $100^\circ$