which of the following quadrilaterals always has diagonals that are perpendicular?

select one:
a. trapezoid
b. rectangle
c. parallelogram
d. rhombus

which quadrilateral only has one pair of parallel sides?

select one:
a. parallelogram
b. rhombus
c. kite
d. trapezoid

in a parallelogram, one side is 10 in and the opposite side is represented as 2x-4. what is the value of x?

select one:
a. 7
b. not enough information to solve.
c. 10
d. 3

Question

which of the following quadrilaterals always has diagonals that are perpendicular?

select one:
a. trapezoid
b. rectangle
c. parallelogram
d. rhombus

which quadrilateral only has one pair of parallel sides?

select one:
a. parallelogram
b. rhombus
c. kite
d. trapezoid

in a parallelogram, one side is 10 in and the opposite side is represented as 2x-4. what is the value of x?

select one:
a. 7
b. not enough information to solve.
c. 10
d. 3

Accepted Answer

{ "quality": "clear", "question_count": 3, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Quadrilateral Properties", "Trapezoid Definitions", "Parallelogram Properties" ], "new_concepts": [ "Rhombus Properties" ], "current_concepts": [ "Quadrilateral Properties", "Trapezoid Definitions", "Parallelogram Properties", "Rhombus Properties" ] } ## Analyze perpendicular diagonals $$ \begin{aligned} &\text{Trapezoid: Diagonals are not generally perpendicular.}\ &\text{Rectangle: Diagonals are congruent, not generally perpendicular.}\ &\text{Parallelogram: Diagonals bisect each other, not generally perpendicular.}\ &\text{Rhombus: Diagonals are always perpendicular.} \end{aligned} $$ ## Analyze parallel sides definition $$ \begin{aligned} &\text{Parallelogram: Two pairs of parallel sides.}\ &\text{Rhombus: Two pairs of parallel sides.}\ &\text{Kite: No pairs of parallel sides.}\ &\text{Trapezoid: Exactly one pair of parallel sides.} \end{aligned} $$ ## Solve for x in the parallelogram $$ \begin{aligned} &\text{Opposite sides of a parallelogram are equal:}\ &2x - 4 = 10\ &2x = 14\ &x = 7 \end{aligned} $$ ## Question 1 a. Trapezoid

b. Rectangle

c. Parallelogram

d. Rhombus ## Question 2 a. Parallelogram

b. Rhombus

c. Kite

d. Trapezoid ## Question 3 a. 7

b. Not enough information to solve.

c. 10

d. 3

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Quadrilateral Properties" ] }

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QUESTION IMAGE

Question

Explanation:

Analyze perpendicular diagonals

Analyze parallel sides definition

Solve for x in the parallelogram

Answer:

Question 1

Question 2

Question 3