Last visit was: 25 Apr 2026, 21:10 It is currently 25 Apr 2026, 21:10
Home
Messages
Tests
Schools
Events
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
User avatar
Skewed
User avatar
Joined: 29 Jul 2007
Last visit: 30 Jul 2008
Posts: 85
Own Kudos:
177
Posts: 85
Kudos: 177
Isosceles Triangle 27 Nov 2007, 15:43
Kudos
Add Kudos
Bookmarks
Bookmark this Post
See diagram.

Please Explain.

Thanks.



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
User avatar
bkk145
User avatar
Joined: 10 Jun 2007
Last visit: 23 Feb 2014
Posts: 645
Own Kudos:
1,801
Posts: 645
Kudos: 1,801
Isosceles Triangle 27 Nov 2007, 18:41
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Skewed
See diagram.

Please Explain.

Thanks.
Show more


B for me.

(1) is not sufficient because if both triangles have the same area, using the area formula, and given that both have the same height, D is the mid point of AC. However, knowing this you cannot tell if the triangle is isso.
INSUFFICIENT

(2) SUFFICIENT because using Pyt theorem, the hyp of each triangle must be the same.
User avatar
Skewed
User avatar
Joined: 29 Jul 2007
Last visit: 30 Jul 2008
Posts: 85
Own Kudos:
177
Posts: 85
Kudos: 177
Isosceles Triangle 27 Nov 2007, 20:12
Kudos
Add Kudos
Bookmarks
Bookmark this Post
bkk145
Skewed
See diagram.

Please Explain.

Thanks.

B for me.

(1) is not sufficient because if both triangles have the same area, using the area formula, and given that both have the same height, D is the mid point of AC. However, knowing this you cannot tell if the triangle is isso.
INSUFFICIENT

(2) SUFFICIENT because using Pyt theorem, the hyp of each triangle must be the same.
Show more


For I, if the areas are the same, then D is the midpoint of AC right. So if AD= CD, then BD would have bisected AC. So isn't BD an angle bisector of angle ABC as well?
User avatar
GK_Gmat
User avatar
Joined: 09 Aug 2006
Last visit: 28 Feb 2009
Posts: 348
Own Kudos:
1,078
Posts: 348
Kudos: 1,078
Isosceles Triangle 27 Nov 2007, 22:27
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Skewed
bkk145
Skewed
See diagram.

Please Explain.

Thanks.

B for me.

(1) is not sufficient because if both triangles have the same area, using the area formula, and given that both have the same height, D is the mid point of AC. However, knowing this you cannot tell if the triangle is isso.
INSUFFICIENT

(2) SUFFICIENT because using Pyt theorem, the hyp of each triangle must be the same.

For I, if the areas are the same, then D is the midpoint of AC right. So if AD= CD, then BD would have bisected AC. So isn't BD an angle bisector of angle ABC as well?
Show more


Yes, according to stat 1, angle ABD = angle DBC. But that does not make the triangle isoceles. That's only one angle of triangle ABD = one angle of triangle DBC.


Stat 1:
Since areas are equal: 1/2 *AD * h = 1/2 DC*h or AD=DC. But we cannot prove similarity or another angle of both triangles equal using this. Insuff.

Stat 2:
angle ABD = angle DBC
angle BDA = angle BDC
Suff.

B
User avatar
Skewed
User avatar
Joined: 29 Jul 2007
Last visit: 30 Jul 2008
Posts: 85
Own Kudos:
177
Posts: 85
Kudos: 177
Isosceles Triangle 27 Nov 2007, 23:29
Kudos
Add Kudos
Bookmarks
Bookmark this Post
GK_Gmat
Skewed
bkk145
Skewed
See diagram.

Please Explain.

Thanks.

B for me.

(1) is not sufficient because if both triangles have the same area, using the area formula, and given that both have the same height, D is the mid point of AC. However, knowing this you cannot tell if the triangle is isso.
INSUFFICIENT

(2) SUFFICIENT because using Pyt theorem, the hyp of each triangle must be the same.

For I, if the areas are the same, then D is the midpoint of AC right. So if AD= CD, then BD would have bisected AC. So isn't BD an angle bisector of angle ABC as well?

Yes, according to stat 1, angle ABD = angle DBC. But that does not make the triangle isoceles. That's only one angle of triangle ABD = one angle of triangle DBC.


Stat 1:
Since areas are equal: 1/2 *AD * h = 1/2 DC*h or AD=DC. But we cannot prove similarity or another angle of both triangles equal using this. Insuff.

Stat 2:
angle ABD = angle DBC
angle BDA = angle BDC
Suff.

B
Show more


But doesn't the height or the altitude have to be perpendicular to the base? Thereby creating a right triangle - ADB = 90=CDB??
User avatar
johnrb
User avatar
Joined: 01 Oct 2007
Last visit: 28 Feb 2008
Posts: 35
Own Kudos:
45
Posts: 35
Kudos: 45
Isosceles Triangle 28 Nov 2007, 00:46
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Skewed
GK_Gmat
Skewed
[quote="bkk145"][quote="Skewed"]See diagram.

Please Explain.

Thanks.

B for me.

(1) is not sufficient because if both triangles have the same area, using the area formula, and given that both have the same height, D is the mid point of AC. However, knowing this you cannot tell if the triangle is isso.
INSUFFICIENT

(2) SUFFICIENT because using Pyt theorem, the hyp of each triangle must be the same.

For I, if the areas are the same, then D is the midpoint of AC right. So if AD= CD, then BD would have bisected AC. So isn't BD an angle bisector of angle ABC as well?

Yes, according to stat 1, angle ABD = angle DBC. But that does not make the triangle isoceles. That's only one angle of triangle ABD = one angle of triangle DBC.


Stat 1:
Since areas are equal: 1/2 *AD * h = 1/2 DC*h or AD=DC. But we cannot prove similarity or another angle of both triangles equal using this. Insuff.

Stat 2:
angle ABD = angle DBC
angle BDA = angle BDC
Suff.

B[/quote]

But doesn't the height or the altitude have to be perpendicular to the base? Thereby creating a right triangle - ADB = 90=CDB??[/quote]

The height does have to be perpendicular to the base--but BD isn't necessarily the height. If ADB and CDB aren't right angles, then you would have to drop a perpendicular from B to an extension of the line AC for the height. (Note that the height of a triangle isn't necessarily contained inside the triangle.)

Another way of looking at it: given statement 1, it's possible that BD is perpendicular to AC, in which case ABC is isosceles. But it's also possible that ABC looks just like the drawing, with AD = CD, but ADB < CDB, so that AB < CB.



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!