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# M01 21

Author Message
Director
Joined: 28 Jul 2011
Posts: 528

Kudos [?]: 282 [0], given: 16

Location: United States
GPA: 3.86
WE: Accounting (Commercial Banking)

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04 Jan 2012, 00:24
Attachments

Geometry.jpg [ 86.16 KiB | Viewed 1087 times ]

_________________

Kudos [?]: 282 [0], given: 16

Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4365

Kudos [?]: 8133 [0], given: 100

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04 Jan 2012, 17:58
Hi, there! I'm happy to help with this.

We are given Triangle ABD with a right angle at B. Then, C is placed on BD, and line AC is constructed.

The question asks: is triangle ABC isosceles. We already know that triangle ABC has one right angle in it at B. A triangle can't have two right angles, so the only way triangle ABC can be isosceles is if AB = BC and, with that, angle BAC = angle ACB, with both of them having a value of 45 degrees. Any information along those lines would help us establish that triangle ABC is isosceles.

Statement #1: Angle ACB is twice as large as angle ADC

We have no idea what the angles are in triangle ADC, so knowing that angle ACB is twice as large as angle ADC tells us nothing about the measure of ACB, nor anything about the relationship of angle ACB and angle CAB. This statement is entirely insufficient.

Statement #2: Angle ACB is twice as large as angle CAB

This tells us a crucial piece of information. Triangle ABC would be isosceles if and only if angles ACB & CAB are congruent. Statement #2 tells us angle ACB is twice as large as angle CAB --- therefore, they are not congruent, therefore triangle ABC is definitely not isosceles. Statement #2 is sufficient for answering the question.

Here's another geometry question, just for practice.

http://gmat.magoosh.com/questions/1009

Does all that make sense? Please let me know if you have any questions.

Mike
_________________

Mike McGarry
Magoosh Test Prep

Kudos [?]: 8133 [0], given: 100

Director
Joined: 28 Jul 2011
Posts: 528

Kudos [?]: 282 [0], given: 16

Location: United States
GPA: 3.86
WE: Accounting (Commercial Banking)

### Show Tags

04 Jan 2012, 18:05
mikemcgarry wrote:
Hi, there! I'm happy to help with this.

We are given Triangle ABD with a right angle at B. Then, C is placed on BD, and line AC is constructed.

The question asks: is triangle ABC isosceles. We already know that triangle ABC has one right angle in it at B. A triangle can't have two right angles, so the only way triangle ABC can be isosceles is if AB = BC and, with that, angle BAC = angle ACB, with both of them having a value of 45 degrees. Any information along those lines would help us establish that triangle ABC is isosceles.

Statement #1: Angle ACB is twice as large as angle ADC

We have no idea what the angles are in triangle ADC, so knowing that angle ACB is twice as large as angle ADC tells us nothing about the measure of ACB, nor anything about the relationship of angle ACB and angle CAB. This statement is entirely insufficient.

Statement #2: Angle ACB is twice as large as angle CAB

This tells us a crucial piece of information. Triangle ABC would be isosceles if and only if angles ACB & CAB are congruent. Statement #2 tells us angle ACB is twice as large as angle CAB --- therefore, they are not congruent, therefore triangle ABC is definitely not isosceles. Statement #2 is sufficient for answering the question.

Here's another geometry question, just for practice.

http://gmat.magoosh.com/questions/1009

Does all that make sense? Please let me know if you have any questions.

Mike

I made a useless mistake in statement 2 i read Angle CAB as CAD and i went wrong on this..........a blunder

But you did offer an amazing explanation

+1 Kudos for You
_________________

Kudos [?]: 282 [0], given: 16

Re: M01 21   [#permalink] 04 Jan 2012, 18:05
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# M01 21

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