Theorems and Properites of Triangles
1. The sum of the three angles of a triangle is equal to 180 degrees.
2. The sum of two sides of a triangle is greater than the third side and their difference is less than the third side.
3.If two sides of triangle are unequal, the angles opposite are unequal and the greater angle is opposite the greater side and conversely.
4. If two sides of a triangle are equal, the angles opposite these sides are equal and conversely. (isosceles triangle)
5. The perpendicular bisector of the sides and the bisectors of the angles of a triangle, meet in points which are the centers of the circumferencial circle and the inscribed circle respectively.
6. The altitudes of a triangle meet on a point. (orthocenter)
7. The medians of a triangle are concurrent at a point which is two-thirds of the distance from any vertex to the midpoint of the opposite side. The point of concurrency is the centroid of the triangle.
8. Two triangles are congruent if two angles and the included side of the one are equal, respectively to two angles and the included side of the other.
9. Two triangles are congruent if two sides and the included angle of the one are equal, respectively to two sides and the included angle of the other.
10. Two triangles are congruent if the three sides of the one are equal, respectively to the three sides of the other.
lessons
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