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m01-q 21

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m01-q 21 [#permalink] New post 25 Dec 2011, 12:48
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In a triangle ABD, B is the right angle. Point C is on BD. If you draw a line from A to C, then is triangle ABC an isosceles triangle?

Angle ACB is twice as large as angle ADC.
Angle ACB is twice as large as angle CAB.

I got the ans but I did not understand something in the explanation for the answer-
the explanation says AB=BC,what theorem or rule is used to get that.
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Re: m01-q 21 [#permalink] New post 29 Dec 2011, 09:26
ashiima wrote:
In a triangle ABD, B is the right angle. Point C is on BD. If you draw a line from A to C, then is triangle ABC an isosceles triangle?

Angle ACB is twice as large as angle ADC.
Angle ACB is twice as large as angle CAB.

I got the ans but I did not understand something in the explanation for the answer-
the explanation says AB=BC,what theorem or rule is used to get that.


err, what is this "something"? Do post the entire explanation.
Please post the figure at least when you post your question.

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Re: m01-q 21 [#permalink] New post 29 Dec 2011, 14:03
ashiima wrote:
In a triangle ABD, B is the right angle. Point C is on BD. If you draw a line from A to C, then is triangle ABC an isosceles triangle?

Angle ACB is twice as large as angle ADC.
Angle ACB is twice as large as angle CAB.

I got the ans but I did not understand something in the explanation for the answer-
the explanation says AB=BC,what theorem or rule is used to get that.



I just did test 1.

For the triangle to be isoceles, the other two angles have to be congruent (both 45 degrees)

#1 doesn't provide any helpful info.
#2 determines that the angles are not congruent, so it cannot be an isoceles triangle. Hope it helps.

Answer is B.

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Re: m01-q 21 [#permalink] New post 11 Mar 2013, 14:10
Hi I just did this problem and I need help understanding why #1 is not sufficient. If B is a right angle, then the triangle can either be a 45-45-90, or a 30-60-90 triangle. If they tell you that angle ACB is twice as large as angle ADB then the only option I can see is for angle ADB to be 30 degrees. If it was 45 degrees then angle ACB would be 90 degrees and that triangle would not be possible. Please explain why I can't infer this information because the answer explanation is not clear. Thanks.
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Re: m01-q 21 [#permalink] New post 12 Mar 2013, 06:13
Expert's post
aryah422 wrote:
Hi I just did this problem and I need help understanding why #1 is not sufficient. If B is a right angle, then the triangle can either be a 45-45-90, or a 30-60-90 triangle. If they tell you that angle ACB is twice as large as angle ADB then the only option I can see is for angle ADB to be 30 degrees. If it was 45 degrees then angle ACB would be 90 degrees and that triangle would not be possible. Please explain why I can't infer this information because the answer explanation is not clear. Thanks.


Attachment:
m01-21.gif
m01-21.gif [ 2.32 KiB | Viewed 509 times ]
Is triangle ABC above an isosceles triangle?

Notice that since ABC is a right triangle then the question basically asks whether angle ACB is equal to angle CAB, because in this case AB would be equal to BC, thus triangle ABC would be an isosceles triangle.

(1) Angle ACB is twice as large as angle ADC --> it certainly possible angle ACB to be equal to angle CAB (45 degrees) and angle ADC to be 22.5 degrees but it's also possible angle ACB NOT to be equal to angle CAB, for example if angle ACB is 60 degrees and angle ADC is 30 degrees. Not sufficient.

(2) Angle ACB is twice as large as angle CAB --> directly says that angle ACB is NOT equal to angle CAB, hence triangle ABC is NOT isosceles. Sufficient.

Answer: B.

Hope it's clear.

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