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chapter 5 (lesson 6 (inequalities in two triangles (hinge theorem:
If two…
chapter 5
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lesson 5
the triangle inequality
The sum of the lengths of any two sides of a triangle must be greater than the length of the third side
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lesson 2
medians, altitudes of triangles
the point of concurrency of the medians of a triangle is called the centroid and is always inside the triangle
An altitude of a triangle is a segment from a vertex to the line containing the opposite side and perpendicular to the line containing that side
A median of a triangle is a segment with endpoints being a vertex of a triangle and the midpoint of the opposite side
The lines containing the altitudes of a triangle are concurrent, intersecting at a point called the orthocenter
lesson 1
bisectors of triangles
Perpendicular bisector theorem:
If a point is on the perpendicular bisector segment, then it is equidistant from the endpoints of the segment
The perpendicular bisector of a side of a triangle does not necessarily pass through a vertex of the triangle.
When three or more lines intersect at a common point, the lines are called concurrent lines.
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lesson 4
indirect proof
Indirect reasoning:
assuming that a conclusion was false and then showing that this assumption led to a contradiction
Indirect proof or proof by contradiction:
temporarily assuming that what you are trying to prove os false
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