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.
+37158 See this:
https://web2.0calc.com/questions/plz-help-with-math-and-please-explain-asap
+130091 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????
