4. Which of the following statements are true?

(A) If a kite is also a parallelogram, then it must be a rhombus.

(B) If a trapezoid is also a parallelogram, then it must be a rhombus.

(C) If a trapezoid is also a kite, then it must be a parallelogram.

(D) If a rhombus is also a trapezoid, then it must be a kite.

Enter your answer as a list, separated by commas.

5. An isosceles trapezoid has side lengths 13,3,13 and 14. What is the perimeter of its Varignon parallelogram?

6. ABCD is a parallelogram such that AB=sqrt(3)*BC. Diagonals line AC and line BD intersect at X and Angle ABC=Angle BXC. Find the measure of Angle ACB in degrees.

Guest Dec 10, 2018

#1**0 **

See this:

https://web2.0calc.com/questions/plz-help-with-math-and-please-explain-asap

ElectricPavlov Dec 10, 2018

#4**+1 **

5. An isosceles trapezoid has side lengths 13,3,13 and 14. What is the perimeter of its Varignon parallelogram?

I didn't actually know what a Varignon parallelogram was.....the parallelogram is formed by joining the midpoints of the sides of the trapezoid...

See the image below :

EFGH is the Varignon parallelogram

A = (0,0)

B = (14,0)

The height of the trapezoid is sqrt (13^2 - 5.5^2] = sqrt (138.5)

C = (8.5, sqrt (138.75) )

D = (5.5, sqrt (138.75) )

In this case, the sides of the parallelogram are congruent....so....we only need to multiply the distance from F to H by 4 to find ts perimeter

F = (5.5/2 , sqrt (138)/2 ) = (2.75, sqrt (138)/ 2 )

H = (7, 0)

So FH = sqrt [ (7 - 2.75)^2 + 138/4 ] = sqrt ( 4.25^2 + 34.5) =

sqrt ( 18.0625 + 34.5) = sqrt ( 56.5625) = 7.25

And the perimeter is 4 times this = 4 * 7.25 = 29 units

P.S. - Just wonder if it's a coincidence that the sum of the lengths of the three shortest sides of the trapezoid = the perimeter of the parallelogram????

CPhill Dec 10, 2018