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In triangle ABC above, what is the length of side BC?

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Status: Stepping into my 10 years long dream
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Re: In triangle ABC above, what is the length of side BC?  [#permalink]

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New post 11 Mar 2018, 02:50
sadikabid27 wrote:
I'm not getting the concept underlying this problem. Could anyone please clarify me that and refer to a particular topic from any book/blog/website to learn this. Thanks .


Hey sadikabid27 ,

Let me explain you.

We need to find out the length of BC.

We already know that BD = BC because triangle BDC is isosceles. --(1)

Also, angle ABD + angle BAD = angle BDC ( Sum of interior opposite angles = Exterior angle.)

=> angle ABD = 2x - x = x.

=> Triangle BDA is also isosceles.

=> AD= BD --(2)

from (1) and (2), we can say

AD = BC.

Now option A is giving us AD, Hence the value will be same for BC. Hence, sufficient.

Option B isn't giving us any length. Hence, insufficient.

Does that make sense?
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Re: In triangle ABC above, what is the length of side BC?  [#permalink]

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New post 11 Mar 2018, 03:00
Thanks for your fast response abhimahna. Maybe, it's very silly of me but I'm not getting these steps
"Also, angle ABD + angle BAD = angle BDC ( Sum of interior opposite angles = Exterior angle.)

=> angle ABD = 2x - x = x.

=> Triangle BDA is also isosceles"
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Re: In triangle ABC above, what is the length of side BC?  [#permalink]

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New post 11 Mar 2018, 03:07
1
sadikabid27 wrote:
Thanks for your fast response abhimahna. Maybe, it's very silly of me but I'm not getting these steps
"Also, angle ABD + angle BAD = angle BDC ( Sum of interior opposite angles = Exterior angle.)

=> angle ABD = 2x - x = x.

=> Triangle BDA is also isosceles"


Hey sadikabid27 ,

You need to learn the properties of the triangles.

One of the properties says : The exterior angle of a triangle is always equal to the sum of the two opposite interior angles.

Check this image:

Attachment:
Untitled.gif
Untitled.gif [ 2.64 KiB | Viewed 415 times ]


Does that make sense?
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Re: In triangle ABC above, what is the length of side BC?  [#permalink]

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New post 11 Mar 2018, 22:53
sadikabid27 wrote:
I'm not getting the concept underlying this problem. Could anyone please clarify me that and refer to a particular topic from any book/blog/website to learn this. Thanks . Bunuel mikemcgarry VeritasPrepKarishma



There are two Geometry concepts being tested here:

1. If two angles of a triangle are equal, sides opposite to them are equal too (isosceles triangle).
2. Measure of the exterior angle is the sum of interior opposite angles. Check this: https://mathbitsnotebook.com/Geometry/S ... Angle.html

Even if you don't know the theorem (point 2), you can easily derive it. The exterior angle BDC makes a straight angle with BDA so their sum will be 180.
BDC + BDA = 180
Also, DAB + ABD + BDA = 180 ( sum of angles of a triangle)

BDC + BDA = DAB + ABD + BDA
BDC = DAB + ABD
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Re: In triangle ABC above, what is the length of side BC? &nbs [#permalink] 11 Mar 2018, 22:53

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