help.............?

Question

1)Some parallelograms are trapezoids.


True
False

2)In which polygon is the sum of the measures of the interior angles 540°?


A. pentagon
B. nonagon
C. heptagon
D. hexagon

3)Every square is a rhombus.


True
False

Answer 1

Hi,

1)Some parallelograms are trapezoids.

False - Parallelograms have to have 2 pairs of parallel opposite sides. Trapezoids only have 1 pair of opposite parallel sides.

2)In which polygon is the sum of the measures of the interior angles 540°?

The sum of the measures in a polygon with "n" sides is

S = 180(n - 2) Filling in 540, you have:
540 = 180(n - 2) Distributing:
540 = 180n - 360 Add 360:
700 = 180n Divide by 180
5 = n This means it has 5 sides so it is a pentagon.

A. pentagon
B. nonagon
C. heptagon
D. hexagon

3)Every square is a rhombus.


True because a rhombus is a parallelogram with 4 congruent sides. A square is also a parallelogram (it has 2 pairs of opposite parallel sides) and it also has 4 congruent sides. Therefore, it is a rhombus too. It's just a rhombus with all right angles.

I hope that helps!! :-)
False

Answer 2

False. A trapezoid always has two non-parallel sides, so it could never be a parallelogram.

540=180(n-2)
540 = 180n -360
900 =180n
5 = n so the answer is pentagon

A rhombus is a quadrilateral with all four sides equal. A square is a quadrilateral with four equal sides. Therefore TRUE, a square is always a rhombus.

Answer 3

1. actually ALL parallelograms are trapezoids, as a trapezoid is defined to have 1 set of parallel sides. Parallelograms have that (and more.) As a side note, some sources claim trapezoids have ONLY 1 set of parallel sides. So it depends on what definition you are using.

2. pentagon

3. True

Answer 4

1 true
2 A
3true

Answer 5

1. definitely false

2. A

3. True