BrainLab wrote:

I have solved this one , but I have one question though... It was not really important (because its a DS) which sides to (short or long leg) to write in tha ratio, BUT for a PS question it's important. HOw one can know which sides are corresponding ? In this picture it's not easy to identify short and long leg....?

Dear

BrainLab,

I'm happy to respond.

We can figure out everything we need about proportional sides by keeping track of the angles. Here's what I mean.

1) Look at the big triangle, ABC. Right angle at B. Say that the angle BAD has a measure of A and the angle DCE has a measure of C. We know that A and C are complementary angles, that is, A + C = 90 degrees. It appears that A > C, which means that BC > AB. Let's assume that is the relationship of these two angles.

2) Look at triangle ABD. Right angle at C. The angle at vertex A still has a measure of A, so the angle at vertex B, angle ABD, just have a measure of C. Again, A > C, so (angle BAD) > (angle ABD), which means that BD > AD.

3) Look at triangle DEC. Right angle at C. The angle at vertex C still has a measure of C, so the angle at vertex D, angle EDC, just have a measure of A. Again, A > C, so (angle EDC) > (angle ECD), which means that EC > DE.

4) Now, look at triangle BED. Right angle at E.

angle (BDE) = 90 - (angle EDC) = 90 - A = C

angle (DBE) = 90 - (angle ABD) = 90 - C = A

Again, A > C, so (angle DBE) > (angle BDE), which means that ED > BE.

Here is a highly accurate diagram of the situation, with the angles color-coded so you can see which angle equals which.

Attachment:

triangle with colored angles.JPG [ 17.12 KiB | Viewed 1377 times ]
Notice that the light green angle (A) plus the purple angle (C) equals a right angle, and that every triangle in the diagram has one light green angle, one purple angle, and one right angle. In each case, the leg opposite the purple angle is less than the leg opposite the light green angle.

Does all this make sense?

Mike

_________________

Mike McGarry

Magoosh Test PrepEducation is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)