mid-segment of a triangle (p. 259)
a triangle that connects the midpoints of two sides.
A midsegment is parallet to the third side, and is half its length.
equidistant (p. 266)
the bisector line is equal distance from the sides of the angle
triangle midsegment theorem (p. 260)
if the segment joins the midpoints of two sides of a triangle, then the segment is parallet to the third side and is half its length.
perpendicular bisector theorem(p. 265)
converse of the above
if the point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.
If point is equidistant from the endpoints of a segment, then it is on the perpendicular besector of the segment.
angle bisector theorem (p.266)
converse of above
if the point is on the bisector of an angle, then the point is equidistnt from the side sof the angle.
if a point in th einterior of an angle is equidistant from the sides of the angle, then the point is on the angle bisector.
centroid (p.274) (also known as the point of concurrency of the medians)
the center of gravity of a triangle - it is the point where a triangular shape will balance. (the point of concurrency of the medians)
median of a triangle (p. 274)
the segment whose endpoints are a vertex AND the midpoint of the opposite side
altitude of a triangle (p. 275)
the perpendicular segment from a vertex to the line containing the opposite side.
It can be the SIDE of a triangle OR it may lie OUTSIDE the triangle.
Comparison Property of Inequality
If a=b+c and c>0, then a>b
Proof of the Comparison Property
Given a=b+c, c>0
1. c>0 1. Given
2. b+c>b+0 2. Addition Property of Inequality
3. b+c>b 3. simplify
4. a=b+c 4. given
5. a>b 5. substitute a for b+c in statemnt 3
corollary to triangle exterior angle theorem (p. 290)
the measure of an exterior angle of a triangle is greater than the measure of each of its remote interior angles
Triangle inequality theorem (p. 292)
the sum of the lengths of any two sides of a triangle is greater than the length of the third side.
the point that divides the segment into two congruent (equal) segments.
negation (p. 280)
statement has opposite truth value.
i.e. Knoxville is the capital of TN is false
Knoxville is not the capital of TN is true (this is the negation statement)
inverse (p. 280)
is a conditional statement which negates both the hypothesis and the conclusion.
i.e. (conditional stmt: if a figure is a square, then it is a rectangle)
inverse of this: If a figure is NOT a square, then it is NOT a rectangle.
contrapositive (p. 280)
a conditional switches the hypothesis and the conclusion and negates both.
i.e. (conditional stmt: if a figure is a square, then it is a rectangle.)
contrapositive of the above: If a figure is not a rectangle, then it is not a square.