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plz help with math questions asap

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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.

Dec 10, 2018

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See this:

Dec 10, 2018
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Those questions weren't answered

Guest Dec 10, 2018
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Sorry......missed that...

ElectricPavlov  Dec 10, 2018
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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????   Dec 10, 2018
edited by CPhill  Dec 10, 2018
edited by CPhill  Dec 10, 2018
edited by CPhill  Dec 10, 2018
edited by CPhill  Dec 10, 2018