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Is quadrilateral ABCD a rectangle?
(1) ABCD is a parallelogram.
(2) ABCD is a square.
(1) ABCD is a parallelogram.
(2) ABCD is a square.
22 Jul 2019, 11:17
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Dillesh4096
Is quadrilateral ABCD a rectangle?
(1) ABCD is a parallelogram.
(2) ABCD is a square.
(1) ABCD is a parallelogram.
(2) ABCD is a square.
Ah, a vocab question in the Quant section. To sort this one out, we need to have a clear understanding of a quadrilateral: a four-sided polygon (any one will do). Looking at Statement (1), a parallelogram must have opposite sides that are parallel, but the standard image of one looks like a square of jello that has been tossed onto a surface from an angle. It could be true that the original shape had been a rectangle, but, leaving the jello analogy behind, for all we know, the shape started off looking skewed. Thus, Statement (1) is NOT sufficient, and we can drop choices (A) and (D).
Looking at Statement (2), if ABCD is a square, then it is game over: all squares are, by definition, rectangles: four-sided polygons with parallel sides opposite each other, whose sides also form 90-degree interior angles at each vertex. The answer must be (B).
For reference, I like the sort of Venn diagram on the following page, in which the various quadrilaterals are neatly categorized:
https://www.math.com/school/subject3/lessons/S3U2L3DP.html
Happy studies.
- Andrew
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