# sophie diagrams

• Jun 8th 2010, 12:14 AM
shanikasamuel
sophie diagrams
hi i need help immediately on this question its due tommorrow:

The diagram below consists of a rectangle ABCD and a triangle DXY so that X and Y are points on the line segments AB and BC respectively and angle DXY = 90 degrees. If all th eline segments in the diagram have integer lenghts, then we call it a sophie diagram.

(i have attached the image of the diagram)

a) Show that DA = AX = XD
XB BY YX
Note: for a) there are supposed to be fraction lines in betweeen but i dont know how to put them in!

Thanks for the Help it means a lot!
• Jun 8th 2010, 01:41 AM
Amer
AXD is similar to XBY why?

we say that two triangles are similar if they have the same angles
from the similar we can solve ur problem
• Jun 8th 2010, 01:51 AM
shanikasamuel
Quote:

Originally Posted by Amer
AXD is similar to XBY why?

we say that two triangles are similar if they have the same angles
from the similar we can solve ur problem

i dont understand what you are saying sorry
• Jun 8th 2010, 01:58 AM
shanikasamuel
Quote:

Originally Posted by shanikasamuel
i dont understand what you are saying sorry

Sorry Amer i get what you were saying now
• Jun 8th 2010, 02:12 AM
Awsom Guy
?
Quote:

Originally Posted by Amer
AXD is similar to XBY why?

we say that two triangles are similar if they have the same angles
from the similar we can solve ur problem

How can you solve that using similar triangles?
• Jun 8th 2010, 02:28 AM
Amer
when two triangles are similar the ratio between the similar sides are equal

in our triangle we have <B = <A = 90
<BXY = <XDA
<BYX = <AXD

so

$\frac{XB}{BY} = \frac{AD}{AX}$

$\frac{XB}{XY} = \frac{AD}{DX}$

like this