![altitude geometry geogebra altitude geometry geogebra](https://www.geogebra.org/resource/x7zGCgNf/JzWNFAz1dyHNeO0m/material-x7zGCgNf.png)
Centers of Triangle On every triangle there are points where special lines or circles intersect, and those points usually have very interesting geometrical properties. You can draw an object with the help of tools or by entering command in the input bar of GeoGebra window. A variable in Geogebra is represented by a slider. For example, f(x) = x 2 4x+2, a quadratic function, is represented by a parabola in graphical view and by an equation in algebraic window. It is capable of representing mathematical objects (at present 2-dimensional) algebraically and geometrically. It is an open source application and is freely available.
#Altitude geometry geogebra software#
Introduction to Geogebra GeoGebra is an educational software for exploring and demonstrating Geometry and Algebra. Let us go through the introduction of Geogebra. If a triangle has its three sides of unequal lengths then it is called a scalene triangle. Triangles which satisfy these conditions are called equilateral triangles. Conversely, if ACB = BAC = CBA then AB = BC = CA. If a triangle ABC satisfies AB = BC = CA then ACB = BAC = CBA. Triangles which satisfy these conditions are called isosceles triangles. If a triangle PQR satisfies PQ = PR then PRQ = PQR. Some basic facts about a triangle are Construction of a triangle is possible only when the sum of lengths of two sides is greater than the third side. The portion of the plane enclosed by the triangle is called the triangle interior, while the remainder is the exterior. The sides of a triangle are given special names in the case of a right triangle, the side opposite to the right angle is called the hypotenuse and the other two sides being known as the legs. Every triangle has three sides and three angles, some of which may be have equal measurements. A simple close curve formed by these three segments is called a triangle. Introduction Mark three non-collinear point P, Q and R on a paper. We will discuss basic facts about triangle first and then see how we can locate centres related to triangle. In this paper, we will explore and visualize various centres of a triangle using Geogebra. In the figure above DE is parallel to BC and DE is half as long as BC.1 Visualizing Triangle Centers Using Geogebra Sanjay Gulati Shri Shankaracharya Vidyalaya, Hudco, Bhilai India ABSTRACT. 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.
![altitude geometry geogebra altitude geometry geogebra](https://www.geogebra.org/resource/acgtjtu7/HvdX55PJDk3dTEHG/material-acgtjtu7-thumb@l.png)
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.
![altitude geometry geogebra altitude geometry geogebra](https://www.geogebra.org/resource/WnHjdEbA/sZNC1ZHrTiLvWsGS/material-WnHjdEbA-thumb@l.png)
![altitude geometry geogebra altitude geometry geogebra](https://www.geogebra.org/resource/rEC83N4b/ELkWxLe5vAMc1Zwf/material-rEC83N4b-thumb@l.png)
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. 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.