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7.2 Parallel Lines and Perpendicular Lines; 7.3 Areas of Polygons; 7.4 Equations of Loci; 8) Vectors 8.1 Vectors; 8.2 Addition and Subtraction of Vectors; 8.3 Vectors in a Cartesian Plane; 9) Solution of Triangles 9.1 Sine Rule; 9.2 Cosine Rule; 9.3 Area of Triangles; 9.4 Application of Sine Rule, Cosine Rule and Area of a Triangles; 10) Index ...
Given that Playfair's postulate implies that only the perpendicular to the perpendicular is a parallel, the lines of the Euclid construction will have to cut each other in a point. It is also necessary to prove that they will do it in the side where the angles sum to less than two right angles, but this is more difficult. [17]
The three perpendicular bisectors meet at the circumcenter. Other sets of lines associated with a triangle are concurrent as well. For example: Any median (which is necessarily a bisector of the triangle's area) is concurrent with two other area bisectors each of which is parallel to a side. [1]
the distance between the two lines can be found by locating two points (one on each line) that lie on a common perpendicular to the parallel lines and calculating the distance between them. Since the lines have slope m , a common perpendicular would have slope −1/ m and we can take the line with equation y = − x / m as a common perpendicular.
If two lines (a and b) are both perpendicular to a third line (c), all of the angles formed along the third line are right angles. Therefore, in Euclidean geometry, any two lines that are both perpendicular to a third line are parallel to each other, because of the parallel postulate. Conversely, if one line is perpendicular to a second line ...
In a Cartesian coordinate system, all coordinates curves are lines, and, therefore, there are as many coordinate axes as coordinates. Moreover, the coordinate axes are pairwise orthogonal. A polar coordinate system is a curvilinear system where coordinate curves are lines or circles. However, one of the coordinate curves is reduced to a single ...