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Triangles properties and types | GMAT GRE Geometry Tutorial

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  7. Triangles is a very simple game. The objective is to make as many triangles as possible, by drawing lines from one dot to another. And that's it. The shortest rule section I've ever written : If you're playing with a mouse you just click on one dot and drag the mouse over to the dot you want to connect to. On a touchscreen you just touch a dot with your finger and drag it over to the other dot.

    This online version of Triangles was made by me, Einar Egilsson.

    Over there on the left is my current Facebook profile picture. This is a game I played when I was a kid in Iceland, with pen and paper. You just put a bunch of random dots on the paper and then start drawing lines. I had forgotten all about it until I saw on Snapchat that a friend was playing it with her kids.

    I played it a few times with my wife and kids and started thinking it could be a nice little game to make for the site. This is the first game I've made for the site that has some dynamic graphics.

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    Triangles classified based on their internal angles fall into two categories: right or oblique. The longest edge of a right triangle, which is the edge opposite the right angle, is called the hypotenuse. Any triangle that is not a right triangle is classified as an oblique triangle and can either be obtuse or acute. There are multiple different equations for calculating the area of a triangle, dependent on what information is known.

    Likely the most commonly known equation for calculating the area of a triangle involves its base, b , and height, h. The "base" refers to any side of the triangle where the height is represented by the length of the line segment drawn from the vertex opposite the base, to a point on the base that forms a perpendicular. Given the length of two sides and the angle between them, the following formula can be used to determine the area of the triangle.

    Note that the variables used are in reference to the triangle shown in the calculator above. Another method for calculating the area of a triangle uses Heron's formula.

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    Unlike the previous equations, Heron's formula does not require an arbitrary choice of a side as a base, or a vertex as an origin. However, it does require that the lengths of the three sides are known. The median of a triangle is defined as the length of a line segment that extends from a vertex of the triangle to the midpoint of the opposing side.

    Living Sound Triangles

    A triangle can have three medians, all of which will intersect at the centroid the arithmetic mean position of all the points in the triangle of the triangle. Refer to the figure provided below for clarification.

    Triangles - Educational Video for Kids

    The medians of the triangle are represented by the line segments m a , m b , and m c. The length of each median can be calculated as follows:. The inradius is the radius of the largest circle that will fit inside the given polygon, in this case, a triangle.

    The inradius is perpendicular to each side of the polygon. In a triangle, the inradius can be determined by constructing two angle bisectors to determine the incenter of the triangle. The inradius is the perpendicular distance between the incenter and one of the sides of the triangle.