Quadrilaterals Quiz:

What is the value of x in parallelogram ABCD below?

Answer

Since this is a parallelogram and we we know that one angle is 90°, all angles must be 90°. Remember consecutive angles in a parellelogram are supplementary and opposite angles are congruent. Therefore, all 4 angles are 90° and this quadrilateral is a rectangle. Also,AEB and AED are supplementary angles, Therefore AED is 130°.Next, remember that the diagonals of any paralleogram bisect each other and the diagonals of a rectangle are congruent. Therefore, AE=ED, making AED is isosceles and DAE = ADE, being base angles of an isoscels triangle. Therefore, x = ½130 = 65°

Prove that A(0,0), B (3,4) , C (7,9) and D (4,5) be a parallelogram?

Answer

To solve this problem use coordinate geometry proof.

• 1) Use the slope formula. The slope of a line = rise/run to establish that opposite sides are parallel

2) Show all work
• The slope of AB = 4/3
• The slope of CD = (9−5)/(7−4) = 4/3
• The slope of AD = 5/4
• The slope of CB= (9 − 4)/(7− 3) = 5/4

Draw a conclusion
• AB || CD and AD || CB because both pairs of opposite sides have the equal slope.
• ABCD is a parallelogram since the opposite sides are parallel

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