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# In the figure above, if the three lines intersect at a point as shown,

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Math Expert
Joined: 02 Sep 2009
Posts: 54368
In the figure above, if the three lines intersect at a point as shown,  [#permalink]

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19 Jul 2017, 02:58
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Difficulty:

35% (medium)

Question Stats:

75% (01:12) correct 25% (01:17) wrong based on 38 sessions

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In the figure above, if the three lines intersect at a point as shown, then a + b must be equal to which of the following?

I. d + e
II. c + f
III. e + f

(A) I only
(B) II only
(C) III only
(D) II and III only
(E) I, II and III

Attachment:

2017-07-19_1357.png [ 7.45 KiB | Viewed 790 times ]

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Joined: 12 Jun 2017
Posts: 9
Re: In the figure above, if the three lines intersect at a point as shown,  [#permalink]

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19 Jul 2017, 03:24
A.
Vertically opposite angles

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Re: In the figure above, if the three lines intersect at a point as shown,  [#permalink]

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25 Jul 2017, 10:57
Bunuel wrote:

In the figure above, if the three lines intersect at a point as shown, then a + b must be equal to which of the following?

I. d + e
II. c + f
III. e + f

(A) I only
(B) II only
(C) III only
(D) II and III only
(E) I, II and III

From the diagram, we see that a = d and b = e, and thus a + b = d + e.

Thus, I is true.

We see that Roman numeral II need not be true if we take, for instance, c = f = 20 and a = b = d = e = 80.

Roman numeral III need not be true either, because if it were, since b = e, we would have a + b = b + f, which implies a = f. We can take values for a, b, c, d, e, and f where a is not equal to f to see that this equality could fail.

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Re: In the figure above, if the three lines intersect at a point as shown,   [#permalink] 25 Jul 2017, 10:57
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# In the figure above, if the three lines intersect at a point as shown,

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