Which statement is true about parallelograms? a. a parallelogram reflected across one of its diagonals is carried onto itself if its adjacent sides are congruent. b. a parallelogram reflected across a line segment joining the midpoints of its opposite sides is carried onto itself. c. a parallelogram reflected across a line segment joining the midpoints of its opposite sides is carried onto itself if its opposite sides are congruent. d. a parallelogram reflected across one of its diagonals is always carried onto itself.

Option B

Step-by-step explanation:

A parallelogram is one where opposite sides are parallel and equal.

Also diagonals bisect each other

SInce parallelogram is not symmetric about diagonal option a cannot be true.

Even if adjacent sides are equal, since diagonals do not bisect angles, the reflection is not exact.

B is true since opposite sides are parallel line segment joining mid points will be a symmetric line

C is false since opposite sides are congruent is superfluous because when parallelogram it is automatically defined as opposite sides equal

D is false as in  a parallelogram diagonal does not divide into two symmetrical figures the parallelogram

.there can be infinite values of m and n that can satisfy the above equation. for each value of m of m or n. there maybe infinite sets of solution for the above

step-by-step explanation:

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240