If I look at the other two altitudes in this obtuse triangles, we're going to have one altitude going like that I'm going to have to extend that side as well and we'll drop down another altitude. Notice that I had to extend that opposite side. So if we pick this vertex, our opposite sides are over here but that opposite side doesn't continue to where this altitude will drop. An altitude of a triangle is a perpendicular segment that joins the vertex of a triangle to the opposite side. So a third case is the obtuse triangle, and here is where I say to a line containing the opposite side. However if I pick my 90 degree angle as my vertex, then we'll be able to see that altitude inside the triangle. If I pick this vertex right here the altitude will just be that leg of the triangle.

That's going to be that leg of the triangle. Definition: an altitude is a segment from the vertex of a triangle to the opposite side and it must be perpendicular to that segment (called the base). If we look at a right triangle over here we can see that if I pick this vertex right here, we already have an altitude drawn. Notice that all three altitudes are inside the triangle. We would have two more altitudes, each of which would go perpendicular to the opposite side. So if I were to pick this top vertex right here, the altitude would go straight down perpendicular to the opposite side. So if we look at an acute triangle, there are going to be three altitudes, one form each vertex. It's not always to the opposite side and you're going to see why in a second here. So this definition is written very carefully. What we're talking about is a perpendicular segment, remember this symbol right here means perpendicular-I'm trying to get you used to seeing these symbols-from a vertex to a line containing the opposite side. One more thing: this will divide-by-zero and fail where points A & B have the same X-value (because it divides by Ax-Bx, which would be zero) but it's a start.When we're talking about triangles, there's a special segment three in each triangle called an 'Altitude.' So we're not talking about skiing here. Print('Intersection at (%s, %s)' % (Dx, Dy)) #Find the intersection of the two lines AB & CD:ĭx = (Y_intercept_CD - Y_intercept_AB)/(slope_AB - slope_CD) Altitude is a term used to identify heights of objects such as airplanes, space shuttles, rockets, atmospheric balloons and heights of places such as atmospheric layers and clouds. Most of the time, this reference point is the mean sea level. Print('CD: slope: %s, intercept: %s' % (slope_CD, Y_intercept_CD)) The definition of altitude is the height measured from a fixed reference point. Print('AB: slope: %s, intercept: %s' % (slope_AB, Y_intercept_AB)) Putting it all together, assume a triangle of A=(-4, 2), B=(0, 6), C=(6, -4): #Points A, B,C: Let's use the one for AB: Dy = slope_AB * Dx + Y_intercept_AB For the Y-value, use either line equation. That will give you the X-value for D ( Dx). The parallel sides can be horizontal, vertical or slanting. The parallel sides of a trapezium are known as the bases, and its non-parallel sides are called legs.

X = (Y_intercept_CD - Y_intercept_AB)/(slope_AB - slope_CD) A trapezoid, also known as a trapezium, is a flat closed shape having 4 straight sides, with one pair of parallel sides. Line AM is the altitude of triangle ABC through A. (slope_AB - slope_CD)*X = Y_intercept_CD - Y_intercept_AB Definition: A triangle is isosceles if two of its sides are equal. slope_AB * X - slope_CD*X = Y_intercept_CD - Y_intercept_AB So now you have equations for line AB and line CD: Y = slope_AB * X + Y_intercept_ABĪnd your problem is simplified to finding where those lines intersect, which is point D.įrom the above equations, since both right-hand sides are equal to Y we can set them equal to each other: slope_AB * X + Y_intercept_AB = slope_CD * X + Y_intercept_CDĪnd now it's just a matter of solving for X. So the equation for CD is Y = slope_CD * X + Y_intercept_CD. First, find its Y-intercept: Y_intercept_CD = Cy - slope_CD * Cx So now, given that you have one point (C) on line CD and its slope, you can get the equation for CD the same way as you did for AB. OK, so now, the slope of the altitude from C to where it intersects line AB (let's call that point D, and the altitude line CD) is the negative reciprocal of the slope of AB so slope_CD = -(1/slope_AB). So the equation for AB is Y = slope_AB*X + Y_intercept_AB. Now the format of a line is Y = MX+B where M is the slope just calculated, and B is the Y intercept, so: Y_intercept_AB = Ay - slope_AB * Ax. Given that you can calculate the slope_AB as (By-Ay)/(Bx-Ax). You have points A and B ( Ax, Ay and Bx, By).

height refers to something measured vertically whether high or low. So first, you can determine the equation for line AB. height, altitude, elevation mean vertical distance either between the top and bottom of something or between a base and something above it. Consider the triangle with vertices at points A, B and C, and you wish to find where the altitude extending from vertex C intersects the line AB.

Altitude geometry def