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# If E is the midpoint of AD, what is the length of EB?

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Math Expert
Joined: 02 Sep 2009
Posts: 58400
If E is the midpoint of AD, what is the length of EB?  [#permalink]

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21 May 2017, 10:57
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Difficulty:

45% (medium)

Question Stats:

56% (01:06) correct 44% (01:13) wrong based on 149 sessions

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If E is the midpoint of AD, what is the length of EB?

(1) ∠D = 60°
(2) DC = 4

Attachment:

2017-05-21_2155.png [ 6.28 KiB | Viewed 1985 times ]

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Re: If E is the midpoint of AD, what is the length of EB?  [#permalink]

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21 May 2017, 11:19
Since both EB and DC are perpendicular on the same line, EB is parallel to DC.
Thus angle AEB = angle ADC (corresponding angles)

Also by mid point theorem of a triangle, since E is the mid point of AD and EB||DC,
B must be the mid point of AC and EB = DC/2

Statement 1. angle ADC = 60 , so angle AEB is also = 60
Triangle AEB is a 30-60-90 triangle. So we know the ratio of sides of this triangle.
But since none of the three sides is given, we cannot find anything. So Insufficient

Statement 2. DC = 4, so EB = DC/2 = 2 (mid point theorem)
Sufficient

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Re: If E is the midpoint of AD, what is the length of EB?  [#permalink]

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21 May 2017, 12:12
Bunuel wrote:

If E is the midpoint of AD, what is the length of EB?

(1) ∠D = 60°
(2) DC = 4

Attachment:
2017-05-21_2155.png

I think b alone is sufficient as it provides measure of a side.
Triangles AEB and ADC are similar(Angle A is common, Angle b and c are 90 degrees, angle E and D will be equal)
AE/ED=EB/DC
1/2=EB/4
EB=2.

Please correct me if i am wrong.
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Re: If E is the midpoint of AD, what is the length of EB?  [#permalink]

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24 May 2017, 20:55
stat1: gives info about angles..no info on length ..not suff

stat2: EB and DC are parallel,,, using Basic proprtionality theorem,, EB = 1/2 DC,...suff

ans B
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Re: If E is the midpoint of AD, what is the length of EB?  [#permalink]

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06 Sep 2017, 22:23
Bunuel wrote:

If E is the midpoint of AD, what is the length of EB?

(1) ∠D = 60°
(2) DC = 4

Attachment:
2017-05-21_2155.png

If we understand that these are similar triangles and that EB is the midline, then we can clearly see that EB must be half of AD in order to maintain similarity and proportionality.

B
Re: If E is the midpoint of AD, what is the length of EB?   [#permalink] 06 Sep 2017, 22:23
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