In the figure above DE is parallel to BC and DE is half as long as BC. Every mid-parallel is parallel to one of the sides in the triangle and is half the size of the side it runs parallel with. Mid-parallelĪ line that connects the middle of one side with the middle of another side in a triangle is called a mid-parallel. You can also see what happens with an obtuse-angled triangle. In case of an obtuse-angled triangle, the orthocentre will be outside of the triangle. The three altitudes in a triangle will intersect in one point. Sometimes the altitude is called the perpendicular. The shortest distance is always perpendicular to the line. In the figure above, the red part is always half as long as the green part of the median starting in point B.Īn altitude is the shortest distance between a certain point and a line. The medians intersect each other with a ratio of 1 : 2.
The centroid is the centre of gravity of the triangle.įor that reason you can balance the triangle on a sharp tip by putting the triangle with its centroid exactly on the sharp tip. The three medians in a triangle will intersect in one point. Angle AMB angle AMC right angle (so line MA is the perpendicular bisector of BC and also the altitude of ABC through A). Small technicality: when a triangle has weight you actually have a prism. For that reason the weight of the triangle on both sides is also equal, therefore you can balance the triangle on that line. The area on both sides of the median is equal. The median of a triangle is a line through one of the vertices of the triangle to the middle of the opposite side of this vertex. See this in GeoGebra! You can also see what happens with an obtuse-angled triangle. You can use the intersection of the perpendicular bisectors to draw the circumcircle. In case of an obtuse-angled triangle this intersection will be outside the triangle! This is shown in the picture on the left. The three perpendicular bisectors of a triangle will intersect in one point. To construct a perpendicular bisector you need a pair of compasses and a ruler. The perpendicular bisector between two points is a line segment that intersects the line segment between those two points in the middle at an angle of 90 °.īelow you can see the perpendicular bisector of line segment AB.Įvery point on the perpendicular bisector is equidistant to A and B. If you would draw a circle with centre S and radius the shortest distance from S to one of the sides, you will get the incircle of the triangle. The three angle bisectors in a triangle will intersect in one point. To construct an angle bisector you need a pair of compasses and a ruler.
The angle bisector divides an angle into two equal parts.
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