Write equations for three lines that intersect to form a triangle
1 answer:
1.
Any 3 lines a, b and c intersect and form triangles, in no 2 of them are parallel.
2.
2 lines are parallel only if their slopes are equal.
3.
if the equation of a line l is given in the form y=mx+t, then m, the coefficient of x, is the slope of that line.
4.
so given lines a, b, c with equations:
if
, then the lines intersect, forming thus a triangle.
5.
let the 3 lines be:
Any 3 lines a, b and c intersect and form triangles, in no 2 of them are parallel.
2.
2 lines are parallel only if their slopes are equal.
3.
if the equation of a line l is given in the form y=mx+t, then m, the coefficient of x, is the slope of that line.
4.
so given lines a, b, c with equations:
if
5.
let the 3 lines be:
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Check the picture below.
we know that AL is an angle bisector, so the angle at A gets cuts into two equal halves, we also know the angle at B is 30°, so the triangle ABC is really a 30-60-90 triangle, meaning the angle at A is really a 60° angle, cut in two halves gives us 30° and 30° as you see in the picture.
if the angles at A and B, inside the triangle ABL, are equal, twin angles are only made in an isosceles by twin sides, that means that AL = BL.
Looking at the triangle ALC, we can see is also another 30-60-90 triangle, and we can just use the 30-60-90 rule to get x=CL.
