Understanding Parallelograms

What is the defining characteristic of a parallelogram?

• All sides are equal

• Two pairs of parallel sides

• All angles are right angles

• Diagonals are equal

Which property is true for the opposite sides of a parallelogram?

• They are unequal

• They are bisected

• They are congruent

• They are perpendicular

What happens to the diagonals in a parallelogram?

• They are perpendicular

• They are parallel

• They bisect each other

• They are equal

In the example problem, what equation is set up to solve for x?

• 4x - y = 36

• 2x + y = 24

• 4x + y = 24

• 2x + y = 36

What is the value of x when solving 2x + y = 36 and 4x - y = 24?

• x = 20

• x = 15

• x = 10

• x = 5

In the angle problem, what is the quadratic equation formed?

• x^2 + 42 = 13x

• x^2 - 42 = 13x

• x^2 + 13 = 42x

• x^2 - 13 = 42x

What are the possible values of x in the quadratic equation x^2 + 42 = 13x?

• x = 6 or 7

• x = 5 or 6

• x = 8 or 9

• x = 7 or 8

In the proof, which property is used to show that AB is equal to CE?

• Symmetric property

• Transitive property

• Reflexive property

• Substitution property

What is the role of a transversal in the proof involving parallelograms?

• It divides the parallelogram

• It creates parallel lines

• It bisects the sides

• It makes angles equal

Which theorem is used to conclude that sides opposite equal angles in a triangle are congruent?

• Angle sum theorem

• Converse of the isosceles triangle theorem

• Pythagorean theorem

• Triangle inequality theorem