Lesson: Triangles - Part I

Comment on Triangles - Part I

For these difficult questions with the answer choice 'E. Cannot be determined from the information above' - can I assume that for the most part these are 'trap' answer choices? (i.e. test makers know it's not easy so test takers are compelled to say that it cannot be determined using the info given)
gmat-admin's picture

I'm assuming you're referring to Data Sufficiency (DS) questions.

It's true that, for the very hard DS questions, it's more likely that the correct answer is A, B or D. HOWEVER, the problem with this strategy is that the computer adaptive nature of the GMAT ensures that everyone struggles. So, most people may feel that the correct answer to their tricky question will also be more likely to be A, B or D.

sir one more
https://gmatclub.com/forum/if-the-sides-of-a-triangle-have-lengths-x-y-and-z-x-y-113217.html

Hi Brent,

Could you please explain solution to this answer. I am not able to figure it out?
https://gmatclub.com/forum/in-the-figure-above-what-is-the-value-of-x-y-144330.html

Also, Are Similar & Identical triangles one & the same or do they differ? Also, in case of two identical triangles, are their sides equal or are they equal in proportion?
gmat-admin's picture

Question link: https://gmatclub.com/forum/in-the-figure-above-what-is-the-value-of-x-y-...

You bet!
Here's my solution: https://gmatclub.com/forum/in-the-figure-above-what-is-the-value-of-x-y-...

ASIDE: Identical triangles are . . . identical. Their corresponding angles are all equal AND their corresponding sides have equal length.

In SIMILAR triangles, the corresponding angles are equal, and the corresponding sides are PROPORTIONAL to each other.

Here's the video on similar triangles: https://www.gmatprepnow.com/module/gmat-geometry/video/872

https://gmatclub.com/forum/in-triangle-abc-above-what-is-the-length-of-side-bc-168281.html

Do you have a video explanation on this question? I can't seem to understand why statement 1 is sufficient.

Here's my approach:

The information I got from the from the question alone:

For triangle ABC angle ABC = 180 - 3x
Triangle BDC is isoceles with lines BD = CB
Angle DBC = 180 - 4x
Angle ABD = 180 - sum of angles BAD and angles BDA (x + 180 - 2x) = 180 - x
Similarly, Angle DBC would equal 180 - 4x

As such we know that AB = AD and BD = BC
AD is NOT equal to BC (they have different angles to begin with)

So where have I gone wrong?
gmat-admin's picture

Here's my full solution: https://gmatclub.com/forum/in-triangle-abc-above-what-is-the-length-of-s...

Aside: You wrote "AD is NOT equal to BC (they have different angles to begin with)"
Just because sides AD and BC belong to different-looking triangles, doesn't mean they can't have the same length.

Cheers,
Brent

https://gmatclub.com/forum/in-the-figure-shown-above-x-is-the-length-of-side-bd-of-triangle-abd-213796.html hi Brent. Isn't the big triangle ABC isosceles?
So if lengths opposite same angle are same, wouldn't the answer for BD be 4? Cos BC and BD are opposite same angle B ...
gmat-admin's picture

Question link: https://gmatclub.com/forum/in-the-figure-shown-above-x-is-the-length-of-...

Be careful; you are concluding that ∆BDC is isosceles, but this is not necessarily true.

Yes, ∆ABC is isosceles, because AC = BC = 4
However, this does not mean that doesn't mean that ∆BDC is isosceles.
To show that ∆BDC is isosceles, we need to show that it has two equal angles and/or two equal sides.

In fact, side BD cannot be 4, since that would break the rule that says, "If two sides of a triangle have lengths A and B, then:
(DIFFERENCE between A and B) < length of third side < (SUM of A and B)

Cheers,
Brent

Hi Brent,

What are your thought on the question :- https://gmatclub.com/forum/if-abd-is-a-triangle-is-triangle-abc-a-right-?
As per me the answer should be E as B can lie anywhere ?

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