Triangle Inequality Flashcards
Triangle Midsegment Theorem
If a segment joins the midpoints of two sides of a triangle it’s half as long and parallel to the 3rd side
Perp. Bisector
Segment, ray or line, thats perp. to a segment at its midpoint
Perp. Bisector Theorem
if a point is on the perp bisector of a line its equidistant from the endpoints of a segment
perp bisector converse
if a point is equidistant from the endpoints of a line it lies on the perp bisector of that line
angle bisector theorem
if a point is on the angle bisector, its equidistant from the 2 sides of the angle
angle bisector converse
if a point inside the angle is equidistant from the 2 sides of the angle it lies on the angle bisector
circumcenter
point of concurrency of the perp bisectors of a triangle
incenter
point of concurrency of the angle bisecors of a triangle
centroid
point of concurrency of the medians
orthocenter
point of concurrency of the altitudes
concurrency of perp bisectors theorem
circumcenter is equidistant from all sides of a triangle
concurrency of angle bisectors theorem
incenter is equidistant from all sides of a triangle
concurrency of medians theorem
medians of all sides of a triangle intersect at a point 2/3 the distance from each vertex to the opposite side
concurrency of altitudes theorem
lines containing the altitude are concurrent (but may not always be inside the triangle)
comparison prop of equality
if a=b+c then c>0 and a>b
If XZ>XY, then angle Y > angle Z
if 2 sides of a triangle arent equal, the larger angle lies opposite the larger side
largest angle is opposite largest side?
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triangle inequality theorem
the sum of the lengths of any two sides of a triangle is greater than the length of the third side
hinge theorem
if 2 triangles have 2 congruent sides and a non congruent angle, the triangle w the larger angle has the larger side
hinge theorem converse
if 2 triangles have 2 congruent sides and a non congruent angle, the triangle w the larger side has the larger angle
