How to prove that an angle is 90 degrees without using a protractor or having reciprocal slopes as a proof? So the question I have to answer is this: An enlarged view of the daycare patio is shown below that contains two congruent triangles, one of which has been rotated. Using this image, prove that perpendicular lines have opposite and reciprocal slopes.
I know that the slopes are reciprocals, but how do I prove that they are perpendicular? I can't use the reason that the slopes are reciprocals, so I was hoping to say something about how if the angles are 90 degrees they must be perpendicular. Any ideas? Thanks.
BTW I need the answer very soon!
 A: I assume the image shows a square patio $ABCD$ with two triangles in it, probably (ough nothing like that is mentioned in the text) with two legs each on the patio boundary, where one triangle $BGH$ is obtained by rotating the other triangle $AEF$ by 90 degrees around the center $O$ of the patio.
Instead of rotating just one triangle, we could rotatet the figure comprised of $ABCD$ and $AEF$. Then the patio would be left ungchanged (just the vertices rearranged). By the rotation, e.g., line $EF$ and $GH$ are perpendicular (more general, a line and its rotated image always intersect in the rotation angle). Their respective slopes (with respect to a coordinate system that has two of the patio edges lying on the axes) are computed by dividing the (signed) lengths of the interceptions, that is the fisrt slope is $\frac{FA}{AE}$, the second is $\frac{BH}{BG}$. Now use the equality of corresponding sides of congruent triangles.
A: if you just want to prove that they are perpendicular , you can say mid-point of hypotenuse is equidistant from all the points of triangle making it right angle.
