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Is ABC a right triangle? AB = 5; AC = 4. (1) BC = 3 (2) AC = CD

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Joined: 02 Sep 2009
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Is ABC a right triangle? AB = 5; AC = 4. (1) BC = 3 (2) AC = CD  [#permalink]

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New post 05 Nov 2017, 01:02
1
1
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

60% (01:21) correct 40% (01:33) wrong based on 109 sessions

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Re: Is ABC a right triangle? AB = 5; AC = 4. (1) BC = 3 (2) AC = CD  [#permalink]

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New post 05 Nov 2017, 01:21
1
S1: since BC =3, the sides are 3,4,5 which is pythagoras triplet. Hence yes it is right angle triangle. Sufficient
S2 : AC = CD. But it gives no information regarding the triangle ABC, hence it is not sufficient.

Answer is A

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Re: Is ABC a right triangle? AB = 5; AC = 4. (1) BC = 3 (2) AC = CD  [#permalink]

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New post 06 Nov 2017, 09:25
Bunuel wrote:
Image
Is ABC a right triangle? AB = 5; AC = 4.

(1) BC = 3
(2) AC = CD

Attachment:
2017-11-05_1301.png


STATEMENT 1 SATISFY THE PYTHAGORAS THEOREM, SO STATEMENT IS SUFFICIENT.
STATEMENT 2 IS INSUFFICIENT, IT DOES NOT PROVE THAT ABC IS AN RIGHT ANGLE TRIANGLE.
ANSWER IS OPTION A
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Re: Is ABC a right triangle? AB = 5; AC = 4. (1) BC = 3 (2) AC = CD  [#permalink]

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New post 11 Nov 2017, 07:31
1
A because I is sufficient, II does not provide any info about ABC
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Re: Is ABC a right triangle? AB = 5; AC = 4. (1) BC = 3 (2) AC = CD  [#permalink]

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New post 11 Nov 2017, 10:12
2
A is the answer.
3,4,5 is a pythagorean triplet. Statement 1 is sufficient

Statement 2 doesnt mention the lenghts.
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Re: Is ABC a right triangle? AB = 5; AC = 4. (1) BC = 3 (2) AC = CD  [#permalink]

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New post 27 Nov 2017, 22:47
Question has already been answered as A. Though I want to add one thing, which might be useful to someone who doesnt know. In the case we were given that BD=AB (i.e., the bigger triangle ABD is isosceles), then the second statement would have also sufficed on its own to answer this question.

Thats because second statement states that BC is a median (AC=CD), and in an isosceles triangle, median drawn from the vertex of intersection of equal sides (or you can say median from vertex to the non-equal side) acts as a perpendicular bisector also, and divides the bigger isosceles triangle into two congruent right angle triangles.
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Re: Is ABC a right triangle? AB = 5; AC = 4. (1) BC = 3 (2) AC = CD &nbs [#permalink] 27 Nov 2017, 22:47
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Is ABC a right triangle? AB = 5; AC = 4. (1) BC = 3 (2) AC = CD

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