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# If B is the midpoint of AC, what is the length of BE?

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If B is the midpoint of AC, what is the length of BE? [#permalink]  15 Nov 2010, 11:00
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If B is the midpoint of AC, what is the length of BE?

(1) Angel BAE=30
(2) CD = $$\sqrt{20}$$
[Reveal] Spoiler: OA

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Re: Geo [#permalink]  15 Nov 2010, 11:36
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Expert's post
shrive555 wrote:
If B is the midpoint of AC, what is the length of BE?

(1) Angel BAE=30
(2) CD = $$\sqrt{20}$$

why 1 isn't enough ?

As angle E=Angle D then BE||CD. Now as B is the midpoint of AC and BE||CD then BE becomes a midsegment (a line segment joining the midpoints of two sides of a triangle). The property of midsegemnt: the midsegment is always half the length of the third side. So 2BE=CD.

(1) Angel BAE=30 --> triangles BAE and CAD are 30-60-90 triangles where BE is a midsegment. We know only angles but not the lengths, so can not find BE. Not sufficient.

(2) $$CD= \sqrt{20}$$ --> as 2BE=CD then $$BE=\frac{CD}{2}=\sqrt{5}$$. Sufficient.

Check triangles chapter of Math Book for more on this topic: math-triangles-87197.html

Hope it helps.
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Re: Geo [#permalink]  15 Nov 2010, 11:48
Thanks B, Well i was thinking that we know about 30,60,90 as 1:/sqr3:2 ..... But these are ratios of sides only NOT the lengths.
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Re: Geo [#permalink]  16 Nov 2010, 19:12
Expert's post
shrive555 wrote:
If B is the midpoint of AC, what is the length of BE?

(1) Angel BAE=30
(2) CD = $$\sqrt{20}$$

why 1 isn't enough ?

Triangles ABE and ACD are similar (because all corresponding angles are equal)
Since AB is 1/2 of AC, length of BE will be half of length of CD. To know the length of BE, you only need the length of CD.

Knowing only the angle BAE doesn't help because we do not have the length of any side available.
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Re: Geo   [#permalink] 16 Nov 2010, 19:12
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# If B is the midpoint of AC, what is the length of BE?

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