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1. In the parallelogram below, AB is parallel to CD and x-y=40 what is y?

 

2.  Find the area of a rhombus with side length 6 and an interior angle with measure 120 degrees.

 

 

3.  Which of the following statements are true?

(A) A quadrilateral is a parallelogram if it is a rhombus.
(B) A quadrilateral is a rhombus if it is a parallelogram.
(C) A quadrilateral is a parallelogram if and only if it is a rhombus.
(D) A quadrilateral is a rhombus if and only if it is a parallelogram.

Enter all correct options as a list, separated by commas.

 

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
 #1
avatar+18455 
0

1 .    y is much larger than x in the diagram.....how can x-y be positive 40?

 

 

 

2

 Dec 10, 2018
 #2
avatar
0

it is not to scale

Guest Dec 10, 2018
 #5
avatar+18455 
0

More like they are labelled backwards!      cheeky           Wanted to be sure Q was posted correctly....

ElectricPavlov  Dec 10, 2018
 #3
avatar+101871 
+1

2.  Area of rhombus =

 

2 * (1/2) * 6^2 * sin (120)   =   36 sqrt (3)/2 = 18 sqrt(3) units^2

 

 

3.       (A) A quadrilateral is a parallelogram if it is a rhombus.

 

 

cool cool cool


 

 Dec 10, 2018
 #4
avatar+101871 
+1

1. Consecutive angles in a parallelogram are supplemental (sum to 180 degrees)

 

x - y = 40      implies that   x = 40 + y

 

Thus

 

 x + y = 180

 

(40 + y) + y = 180

 

2y + 40  = 180        subtract 40 from both sides

 

2y = 140      divide both sides by 2

 

y = 70°

 

 

 

cool cool cool

 Dec 10, 2018

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