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Re: In the figure above, line segment CZ = 6. What is the length of line [#permalink]

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25 Jun 2017, 10:07

1

This post was BOOKMARKED

In any such question we can use the following trick 1/xy +1/cz = 1/AB, if it is right angled triangle as here so, here cz=6 i.e. 1/xy + 1/6 = 1/AB. ST1- XY=4 SO WE CAN GET AB.- SUFFICIENT ANS IS(A)

How are you proving the big triangles similar to the small triangles? One big and one small is possible but how about the other two?

Responding to a pm:

We are using the AA property of similarity of triangles. When two angles are the same, the third angle would be the same too since the sum of all three angles of each triangle is 180 degrees. And hence the AAA property of similar triangles is satisfied.

In triangles XYZ and BAZ, angles XYZ and BAZ are 90 degrees each. Also, angle BZA and angle XZY are the same angle so they will be equal. So these two triangles are similar by AA.

It is the same logic for triangles CZY and BAY. Angles CZY and BAY are 90 degrees each. Also angles CYZ and BYA are the same angles so they will be equal. So these two triangles are similar by AA.
_________________

In the figure above, line segment CZ = 6. What is the length of line [#permalink]

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19 Sep 2017, 08:00

VeritasPrepKarishma wrote:

sinhap07 wrote:

Leo8 wrote:

Attachment:

FullSizeRender-2.jpg

IMHO - Its A

How are you proving the big triangles similar to the small triangles? One big and one small is possible but how about the other two?

Responding to a pm:

We are using the AA property of similarity of triangles. When two angles are the same, the third angle would be the same too since the sum of all three angles of each triangle is 180 degrees. And hence the AAA property of similar triangles is satisfied.

In triangles XYZ and BAZ, angles XYZ and BAZ are 90 degrees each. Also, angle BZA and angle XZY are the same angle so they will be equal. So these two triangles are similar by AA.

It is the same logic for triangles CZY and BAY. Angles CZY and BAY are 90 degrees each. Also angles CYZ and BYA are the same angles so they will be equal. So these two triangles are similar by AA.

Hi

I get that. But how do we prove the similarity between triangle XYZ and CYZ? Can you pls give the complete solution? How do we even arrive at AB