Presentation on theme: "Median ~ Hinge Theorem. _____(0-10 pts.) Describe what a median is. Explain what a centroid is. Explain the concurrency of medians of a triangle theorem."— Presentation transcript:
Explain the concurrency of medians of a triangle theorem. The point of concurrency of the medians is called the centroid. (Where all median meet.) Centroid Theorem: on every median of any triangle, the distance from the vertex to the centroid is double the distance from the centroid to the midpoint of the opposite side.
Explain what an orthocenter is. Orthocenter: The point of congruency for the 3 altitudes. (where all altitudes meet) The orthocenter of an acute triangle is inside the triangle. The orthocenter of a right triangle is on the vertex of the 90 degrees angle. The orthocenter of an obtuse triangle is on the outside of the triangle.
_____(0-10 pts.) Describe the hinge theorem and its converse. Give at least 3 examples.
Hinge theorem and its converse. If the two sides of two triangles are congruent but the third side is not congruent, then the triangle with the longer side, will have a larger included angle. Converse: If two sides of one triangle are congruent to two sides of another triangle and the tird sides are not congruent, then the larger included angle is across from the longer third side.