Question: Triangles with Intersection

Hi Kai,

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

Cheers,
Brent

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

∠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

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

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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

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

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

If you can mentally move and flip a triangle so that the two triangles look more similar, then that will definitely help.
Nice work!!

This is a great question!
Here's my solution: https://gmatclub.com/forum/in-triangle-abc-above-if-ad-bc-what-is-the-va...