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I understand essentially the whole proof except this one thing it says at the beginning. This bit:

**'If AB makes an angle theta with the x-axis then CD makes an angle theta with the y axis.'**

**So my question is this:**Why do the x and y axis make the same angle (theta) when they intersect AB and CD? What's the reason/proof behind that?

Will be very grateful if anyone can explain this clearly to me:)

__Here is the link to my textbook (go to slide 79 - the bit on perpendicular lines at the bottom):__http://www.slideshare.net/mobile/Slyscott12/core-maths-for-a-level-3rd-edition-by-lbostock-schandler

__Here is the proof typed out:__

Consider the perpendicular lines AB and CD whose gradients are m1 and m2 respectively.

If AB makes an angle theta with the x axis then CD makes an angle theta with the y axis. Therefore triangles PQR and PST are similar.

Now the gradient of AB is ST/PS=m1

And the gradient of CD is - PQ/QR=m2,i.e PQ /QR= - m2

But ST/PS=QR/PQ (since triangles PQR and PST are similar)

Therefore m1= - 1/m2 or m1 *m2 = - 1