Question: Triangles with Intersection

Comment on Triangles with Intersection

When two triangles are similar and we are taking the ratio of the sides. Is it the bigger triangle over smaller or vice versa?

My solution:
x/12 = 5/10
x = 6
greenlight-admin's picture

It doesn't matter whether you compare the bigger triangle over smaller or vice versa; the outcome will be the same in both cases. However, when comparing sides, you must compare CORRESPONDING sides. You have not done so.

The side with length 12 (in the larger triangle) does not correspond to the side with length x (in the smaller triangle).The side with length 12 is between the angles denoted with a check mark and a DOT, whereas the side with length x is between the angles denoted with a check mark and a HEART. As such, those two sides are not CORRESPONDING, which explains why your solution is incorrect.

Does that help?

Thankyou :-) Awesome videos helping me a lot during my prep

Where are the 1200 + practice questions located ?
greenlight-admin's picture

Most of the 1200 practice questions can be found in the Related Resources box beneath most video lessons (e.g.,

These questions help to reinforce the concepts/strategies covered in that particular lesson. You will find that I have personally answered most of those linked questions, using the strategies covered in the video lessons.

It's also important to note that most of those practice questions are official GRE questions, which are (of course) the most representative of what you will see on test day.

Awesome. Nice explanation, thanks.

I got the similar result as Sneha but I have a slightly different explanation. Can we make the smaller triangle CED flip upside down? If we imagine that then the triangle CED will look exactly similar to triangle AEB and also the side CE corresponds to AE and similary DE corresponds to BE. When I take the ratio CE/AE= DE/BE, I too get the same result of 6. So as per your explanation, a proper correspondency only happens when the two sides and the angle within them match and are equal? So we should not only see the sides but also the angles within them. Is this understanding correct? One more question- Is this theory pointing to the SAS,AAS,SSA, etc. these properties? Please clarify.
greenlight-admin's picture

Hi Deepak,

Be careful; side CE does NOT correspond to side AE.

To determine which sides correspond, we must examine where each side lies in relationship to the given angles.

At 1:00 in the video, I have used dots, hearts and check-marks to label all of the angles and show which angles the two triangles have in common.

Notice that side CE lies between the angles denoted with a dot and a check-mark.

So, the side that corresponds to side CE will be side on the big triangle that also lies between the angles denoted with a dot and a check-mark. That side is EB

So, side CE corresponds to side EB (not AE, as you suggest)

ASIDE: The rules (SAS, ASA and SSS) apply to CONGRUENT triangles (i.e., triangles that are EXACTLY the same).
The key concept is this question is the concept of SIMILAR triangles (triangles that share the same angles, but are different sizes)

Does that help?


Yes, that really helps. I understand the difference of congruency and similar triangles now. :) Thank you so much. Also, do we need to know the congruency properties as well for GRE?
greenlight-admin's picture

No, you don't need to know the congruency properties.

Thank you :)
In this question did you mean both triangles have angle B or E because i can't seem to understand how both triangles have angle B
greenlight-admin's picture

I'll direct you to my solution at

Let's first focus on ∆EAF
If we let ∠E = star, and we let ∠F = face, then ∆EAF has the following 3 angles: star, face and 90°
This means star + face + 90° = 180° (angles in a triangle add to 180°)

Now let's focus on ∆EBC
∠E is the same as in ∆EAF. So, ∠E = star
Also notice that ∠C = 90°
KEY: We can already see that ∆EBC shares 2 of its angles with ∆EAF
This means the 3rd angle (∠B) must also be the same as in ∆EAF
In other words, ∠B = ∠F = face

Does that help?


please I had x=6
greenlight-admin's picture

I'm assuming that you incorrectly concluded that side AE and side EC are corresponding sides, which they are not.

Side AE lies between the HEART symbol and the CHECK MARK symbol.
Side EC lies between the CIRCLE symbol and the CHECK MARK symbol.
As such, sides AE and EC are not corresponding sides.


Have a question about this video?

Post your question in the Comment section below, and a GRE expert will answer it as fast as humanly possible.

Change Playback Speed

You have the option of watching the videos at various speeds (25% faster, 50% faster, etc). To change the playback speed, click the settings icon on the right side of the video status bar.

Let me Know

Have a suggestion to make the course even better? Email us today!

Free “Question of the Day” emails!