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09 Feb 2012, 18:40
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C
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Difficulty:
75%
(hard)
Question Stats:
45% (01:27) correct
55%
(01:25)
wrong
based on 383
sessions
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Not Attempted Yet
Is the triangle ABC, right angled at B?
(1) Two interior angles of the triangle ABC are complementary.
(2) In the triangle ABC the length of the median drawn on side AC is shorter than the median drawn on side AB or BC.
(1) Two interior angles of the triangle ABC are complementary.
(2) In the triangle ABC the length of the median drawn on side AC is shorter than the median drawn on side AB or BC.
09 Feb 2012, 19:03
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Is the triangle ABC, right angled at B?
(1) Two interior angles of the triangle ABC are complementary --> complementary angles are two angles that add up to 90° (whereas supplementary angles are two angles that add up to 180°). Since the sum of the angles of the triangle is 180° and two angles add up to 90° then the third angle must be 90°. Though we don't know which one. Not sufficient.
(2) In the triangle ABC the length of the median drawn on side AC is shorter than the median drawn on side AB or BC. Now, the larger an angle, the longest the side opposite that angle and the shorter the median drawn to this side, basically the shortest of the medians of the triangle is the one drawn to the longest side. From this we know that AC is the longest side and opposite the largest angle B. Still insufficient as we don't know the measure of B.
(1)+(2) From (1) one of the angles must be 90° and from (2) angle B is the largest angle, hence angle B = 90°. Sufficient.
Answer: C.
Hope it's clear.
(1) Two interior angles of the triangle ABC are complementary --> complementary angles are two angles that add up to 90° (whereas supplementary angles are two angles that add up to 180°). Since the sum of the angles of the triangle is 180° and two angles add up to 90° then the third angle must be 90°. Though we don't know which one. Not sufficient.
(2) In the triangle ABC the length of the median drawn on side AC is shorter than the median drawn on side AB or BC. Now, the larger an angle, the longest the side opposite that angle and the shorter the median drawn to this side, basically the shortest of the medians of the triangle is the one drawn to the longest side. From this we know that AC is the longest side and opposite the largest angle B. Still insufficient as we don't know the measure of B.
(1)+(2) From (1) one of the angles must be 90° and from (2) angle B is the largest angle, hence angle B = 90°. Sufficient.
Answer: C.
Hope it's clear.
General Discussion
03 Jul 2013, 14:59
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Bunuel
Bunuel,
Can you help to draw figure for Stmt 2? I am not very clear..
