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13 Feb 2018, 22:59
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
65% (01:58) correct
35%
(01:54)
wrong
based on 62
sessions
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Not Attempted Yet
In the figure, AB = BC and angles BAD and BCD are right angles. Which one of the following conclusions may be drawn?
(A) The measure of angle BCA = the measure of angle CAD
(B) The measure of angle B is greater than the measure of angle D
(C) AC = CD
(D) AD = CD
(E) BC is shorter than CD
Attachment:
2018-02-14_0957.png [ 8.72 KiB | Viewed 5898 times ]
13 Feb 2018, 23:43
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Bunuel
As there don't seem to be special symmetries (like regular polygons), we'll look for specific Geometric rules.
This is a Precise approach.
Since AB = BC then the base angles of triangle BAC are equal.
This mean that the base angles of triangle DCA must also be equal as they complement those of BAC to 90 degrees.
Therefore, AD = CD, answer (D).
The only other fact that we know about the figure is that angle ABC and angle CDA sum to 180 (because the 4 angles of a quadrilateral sum to 360) but as this does not appear in any of the answer choices it is not helpful.
17 Feb 2018, 09:47
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Since AB=BC so Angle BCA=angle BAC and since Angle BCD=angle BAD=90 So CAD=ACD thus AD=CD
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