Question: Triangles with Intersection

Comment on Triangles with Intersection

Hi Brent, can we conclude that AB and CD are parallel from the given information? And since angles BAD and ADC both also intersect line segments AB and CD, we can say that they are also equal? The method of recognising similar triangles is the same but is there anything wrong about this way of recognising them?
Thanks for these videos, they are a great help!
Kai
gmat-admin's picture

Hi Kai,

You are correct; AB and CD are parallel, because we're told that ∠ABC = ∠BCD

Cheers,
Brent

Brent,

Could you explain me in a different way from the OG17 Solution. Exercise #138 OG17.

Thanks,
Pedro
gmat-admin's picture

Hi Pedro,

You'll find my step-by-step solution here: https://gmatclub.com/forum/figures-x-and-y-above-show-how-eight-identica...

Cheers,
Brent

Hi Brent, Can we consider ∠BAD equal to ∠CDA as they are vertically opposite?
gmat-admin's picture

∠BAD and ∠CDA aren't vertically opposite.

∠AEB and ∠CED are vertically opposite.

More here: https://www.gmatprepnow.com/module/gmat-geometry/video/858 (the part about vertically opposite angles starts at 4:20 in the video)

Cheers,
Brent

hey brent, how do u know whether to do 5/12=x/10 or 12/5=10/x? either way you get the same result, so does it even matter? or will there be questions where it will matter?

thanks

Yianni
gmat-admin's picture

Great question,Yianni!!

As long as your ratios on each side have the same structure, EITHER equation works.

OPTION #1: We can have "(length of one side of BIG triangle)/(length of corresponding side of SMALL triangle) = (length of another side of BIG triangle)/(length of corresponding side of SMALL triangle)

In this case, we get: 12/5 = 10/x

When we solve this, we get: x = 25/6

-----------------------------

OPTION #2: We can have "(length of one side of SMALL triangle)/(length of corresponding side of BIG triangle) = (length of another side of SMALL triangle)/(length of corresponding side of BIG triangle)

In this case, we get: 5/12 = x/10

When we solve this, we still get: x = 25/6

Does that help?

Cheers,
Brent

perfect! thanks a lot!

https://gmatclub.com/forum/in-triangle-abc-d-is-the-mid-point-of-bc-and-e-is-the-mid-point-of-ad-240720.html
not able to solve this one
sir is this gmat level question?
gmat-admin's picture

Here's my solution: https://gmatclub.com/forum/in-triangle-abc-d-is-the-mid-point-of-bc-and-...

This is a crazy hard question. As I mention in my post, I'd say "skirting the 800 level of difficulty!"

Cheers,
Brent

In the case of congruent triangles, does the GMAT only draw a relationship for parallel lines and triangles sharing two / three angles? What about the other cases to prove congruency - e.g. three sides, two sides and one angle, two angles and one side and two angles with one side?
gmat-admin's picture

I'm not sure whether you meant to say CONGRUENT or SIMILAR.

That said, there are many different ways for the test-maker to create two triangles that are similar (and congruent). Using parallel lines (as in the above video question) is just one of the ways.

Cheers,
Brent

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