similar triangles example 24/07/21
line g has slope m, another line h forms a 45 degree angle with g, find the slope of h in terms of m
Step 2 drop perpendicular from to the x-axis and call that point . then the slope of g is .
Step 3 construct a line at perpendicular to g and call the intersection point of that line with h .
Then the slope of h is
Step 5 construct such that lies on line and
Step 6 because and so
Step 7 by AAA(angle-angle-angle)
Step 8 because is a right isosceles triangle
Step 9 this implies that and are congruent by ASA (angle-side-angle)
Step 10 since and are parallel and and are parallel is a rectangle so . Additionally since is a straight line .
putting it together we get what is shown on the applet
You can generalize this for arbitrary angles as well
if you have any questions or comments you can ask me next friday