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Is quadrilateral ABCD a rectangle?

This topic has 1 expert reply and 0 member replies
ahmedshafea Junior | Next Rank: 30 Posts
Joined
30 Aug 2017
Posted:
19 messages

Is quadrilateral ABCD a rectangle?

Post Mon Sep 11, 2017 12:45 pm
Is quadrilateral ABCD a rectangle?

(1) The diagonals (AC and BD) are perpendicular to each other
(2) The sum of any 3 angles in the quadrilateral is 270 degrees

What's the best way to determine whether statement 1 is sufficient?

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Top Reply
Post Tue Sep 12, 2017 11:43 am
The easiest way to determine whether statement 1 is sufficient is to draw out possible options:

ttps://postimg.org/image/sn4dkljpx/" target="_blank">

Starting with two perpendicular diagonals that are the same length and intersect at their midpoints gives a square, which is a rectangle.

However, changing the length and midpoints of the lines gives:

ttps://postimg.org/image/blg4w8u8l/" target="_blank">

Which is not a rectangle.

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