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In the figure above, x = y = z, and AD = BD. Which of the following mu

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In the figure above, x = y = z, and AD = BD. Which of the following mu [#permalink]

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In the figure above, x = y = z, and AD = BD. Which of the following must be true?

I. AD is parallel to BE
II. DB is parallel to EC
III. Points A, B and C lie on the same line

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


[Reveal] Spoiler:
Attachment:
2017-08-01_2037.png
2017-08-01_2037.png [ 9.7 KiB | Viewed 410 times ]
[Reveal] Spoiler: OA

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Re: In the figure above, x = y = z, and AD = BD. Which of the following mu [#permalink]

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New post 01 Aug 2017, 09:16
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Since x=y, it is possible to say that AD is parallel to BE.
Similarly knowing y=z, we can say that DB is parallel to EC.

Also, points A and B are on the same line as AD=BD, but
because we have no information about BE and EC,
and we cannot say anything about points B and C.

Hence Option C(I and II only) should be our correct answer.
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Re: In the figure above, x = y = z, and AD = BD. Which of the following mu [#permalink]

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New post 01 Aug 2017, 10:46
Since we know x=y we can see that if we extend line BD, then the angles formed by this line that intersects the two lines (AD and BE) follow the parallel line rules therefore AB is parallel to BE. Similarly since y=z, BD is parallel to EC.

Since AD=BD we know that A and B lie on the same line. But we don't know anything about DE or EC so we can't say that C lies on the same line as A and B.

Therefore the answer is C imo.
Re: In the figure above, x = y = z, and AD = BD. Which of the following mu   [#permalink] 01 Aug 2017, 10:46
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