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two coplanar angles with a common side, a common vertex, and no common interior points
a line, segment, or ray that is perpendicular to the segment at its midpoint, thereby bisecting the segment.
law of detachment
if a conditional is true and its hypothesis is true, then its conclusion is true. (if p -> q is true and p is true then q is true)
triangle exterior angle theorem
the measure of each exterior angle of a triangle equals the sum of the 2 remote interior angles
polygon exterior angle theorem
the sum of the measure of the exterior angles of a polygon, one at each vertex, is 360
isosceles triangle theorem
if two sides of a triangle are congruent, then the angles opposite those sides are congruent
if the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and leg of another right angle, then the triangles are congruent
if a segment joins the midpoints of 2 sides of a triangle, then the segment is parallel to the third side and half its length
a segment that has a vertex of a triangle and the midpoint of the opposite side as its endpoints
point where the perpendicular bisectors intersect; perpendicular bisectors are concurrent at this point that is equidistant from the vertices
point where the angle bisectors intersect; angle bisectors are concurrent at this point that is equidistant from the sides
the length of the segment from the vertex to the centroid is twice the length of the segment from the centroid to the midpoint
triangle inequality theorem
the sum of the lengths of any two sides of a triangle is greater than the third side
opposite sides are congruent, opposite angles are congruent, diagonals bisect eachother, if three or more parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal
each diagonal of a rhombus bisects two angles of the rhombus; the diagonals of a rhombus are perpendicular
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