SOLUTION: Hello there! This is a question I had on a test review worksheet, that i didn't quite understand.
"Quadrilateral ABCD is a parallelogram. If adjacent angles are congruent, whic
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Question 571359: Hello there! This is a question I had on a test review worksheet, that i didn't quite understand.
"Quadrilateral ABCD is a parallelogram. If adjacent angles are congruent, which statement must be true?"
A: Quadrilateral ABCD is a square
B: Quadrilateral ABCD is a rhombus
C: Quadrilateral ABCD is a rectangle
D: Quadrilateral ABCD is an isosceles trapezoid
I have eliminated "B" and "D", but I am unsure as to whether ABCD is square or rectangle. Could you kindly explain as to why it is either one?
Found 2 solutions by Alan3354, solver91311:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
"Quadrilateral ABCD is a parallelogram. If adjacent angles are congruent, which statement must be true?"
A: Quadrilateral ABCD is a square
B: Quadrilateral ABCD is a rhombus
C: Quadrilateral ABCD is a rectangle
D: Quadrilateral ABCD is an isosceles trapezoid
I have eliminated "B" and "D", but I am unsure as to whether ABCD is square or rectangle. Could you kindly explain as to why it is either one?
----------------
A parallelogram's sides can be of unequal lengths, so it is not necessarily a square. That leaves rectangle.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The key phrase in the question is "must be"
You don't know anything about the relative measures of the adjacent sides, so while the figure certainly could be a square, or a rhombus for that matter since a square is just a special case of the rhombus, the congruence of adjacent angles demands that the quadrilateral be at least a rectangle.
In fact, your quadrilateral could be a trapezoid because there is some disagreement on the allowed number of parallel sides in a trapezoid. At issue is whether parallelograms, which have two pairs of parallel sides, should be counted as trapezoids. Some authors define a trapezoid as a quadrilateral having exactly one pair of parallel sides, thereby excluding parallelograms. Other authors define a trapezoid as a quadrilateral with at least one pair of parallel sides, making the parallelogram a special type of trapezoid (along with the rhombus, the rectangle and the square). The latter definition is consistent with its uses in higher mathematics such as calculus. The former definition would make such concepts as the trapezoidal approximation to a definite integral ill-defined.
John
My calculator said it, I believe it, that settles it
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