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Mathematics · Class 9
If two lines have slopes m1 and m2, the tangent of the angle theta between them is |m2-m11+m1 m2| when 1+m1 m2 != 0. If 1+m1 m2 = 0 they are perpendicular (already a page). A family of lines shares a form with a parameter, such as y = mx + 2 (all slopes, same intercept 2).
PracticeAn angle bisector is the ray that splits an angle into two equal angles. To draw it: open a compass at the vertex and cut both arms with the same arc; from those two cut points draw equal arcs that meet; the line from the vertex through that meeting point is the bisector. In a triangle the three angle bisectors are concurrent. Their common point is the in-centre. The in-centre is always inside the
PracticeAngle of elevation is the angle up from the horizontal to a line of sight (you look up at a tower). Angle of depression is the angle down from the horizontal (you look down from a cliff). The two are equal when they are alternate angles on parallel horizontals.
PracticeAn angle is formed by two rays that share a common vertex. One ray is the initial arm and the other is the terminal arm. A positive angle is measured anti-clockwise from the initial arm. A negative angle is measured clockwise. In standard position the vertex sits at the origin and the initial arm lies along the positive x-axis. That placement lets you read an angle on the coordinate plane and late