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## Comment on

Triangles with Shared Vertex## straight away we can conclude

## I'm not quite sure what you

I'm not quite sure what you mean by "x will be smaller compare to y, since it forms line of length 3"

## consider line A with length 3

If we have projection of endpoints as a line to form an angle ( analogy: in case

of circle, we have inscribed angle for a chord ), when line is smaller, obviously

angle formed will be lesser, compare to the angle formed by larger line.

therefore angle x is smaller than angle y, since angle x is formed by line 3 units and angle y is formed by line 5 units.

## Sorry, It's still not 100%

Sorry, It's still not 100% clear to me. Are you referring to the rule stated at 0:48?

## yes.

It would be better if i can upload the diagrams.

My assumption was, in general if we have 2 lines with length difference. say one is 2 and other is 5. will project lines at both endpoints with same angle. Those projected lines will meet at some point, forms arbitrary angle. on that case we can tell smaller length line would form smaller angle and larger one would form larger angle.

correct me, if anything wrong.

## I think that sounds correct :

I think that sounds correct :-)

## Is this assumption correct?:

## The rule you are applying

The rule you are applying applies to ONE triangle, but you are using it for TWO triangles. In a single triangle, the angle opposite the longest side will be the greatest angle.

However, we can't then apply this concept to compare an angle in one triangle with an angle in a different triangle.

## angle x = angle X. Vertically

## Yes, that approach is correct

Yes, that approach is correct.

## Also why haven't you compared

## Once we know that triangle

Once we know that triangle ABC has sides with length 2, 3 and 4, we can just use the triangle property described 1:02 at in the following video: https://www.greenlighttestprep.com/module/gre-geometry/video/860

## Not this, I meant you have

## Which triangle property are

Which triangle property are you referring to?

At 0:32 in the video, we conclude that, since ∠ABC = ∠CED, line AB is PARALLEL to line DE

Once we know that AB || DE, we can see that ∠BAC is equal to ∠CDE (at 0:37 in video)

At this point, we have labeled all 3 angles in ∆ABC.

At this point, we COULD use similar triangle to find the lengths of the sides on ∆CDE, but there's really no need to, since ∆ABC already provides all of the information needed to answer the question.

## Hi Brent How will this

I see BE and AD are intersecting at C so from RULE-

"Opposite Angles are equal for intersection lines"

I say <BCA = <DCE =x

Now both Triangles have both the angles in common x,k So I say they are similar. From the RULE, "When 2 angles in similar triangles are equal then their 3rd angle must also be equal".

I conclude that left over 3rd angle in Triangle CBA is y.

Now In Triangle CBA I have all 3 angles and side So from RULE, "The greatest side in a triangle will have greatest opposite Angle and vice versa". Finally y is grater than x

## That's a perfectly valid

That's a perfectly valid solution. Nice work!

## I re-draw the triangles in a

## That's correct.

That's correct.

## So for this problem what I

## Sorry ravin654, but I'm not

Sorry ravin654, but I'm not sure what you're asking. Can you rephrase your question?

## So my question is the reason

## Thanks for the clarification.

Thanks for the clarification.

I believe you may be confusing the triangle property noted at 1:01 in this video https://www.greenlighttestprep.com/module/gre-geometry/video/860 with a different property regarding similar triangles covered here: https://www.greenlighttestprep.com/module/gre-geometry/video/872

The first property allows us to the compare sides and angles in ONE triangle, and the second property allows us to compare sides in TWO similar triangles.

Does that help?