orthocenter/incenter/proofs terms

perpendicular bisectors point of concurrency is…

circumcenter: the circumcenter of a triangle is equal distance from the vertices of a triangle.

obtuse angled triangle: circumcenter lies outside of the triangle

right angled triangle: circumcenter lies on the hypotenuse of a triangle

angle bisectors point of concurrency is…

incenter: the incenter of a triangle is equal distance from the sides of the triangle

the incenter always lies within the triangle

medians point of concurrency is…

centroid: the centroid of a triangle is two-thirds of the distance from each vertex to the midpoint of the opposite side.

centroid always lies within the triangle

centroid always divides each median into segments in the ratio of 2:1

the point of concurrency in altitude is…

orthocenter: the orthocenter of a triangle is that the lines containing altitudes of a triangle are concurrent at the orthocenter.

obtuse angled triangle: orthocenter lies outside the triangle

subtraction postulate

If a = b and c = d, then a-c = b-d; if equal amounts are subtracted from equal amounts, then the differences are equal.

multiplication postulate

If a = b and c = d then ac = bd; if equals are multiplied by equals, then the products are equal

division postulate

if a = b and c = d, then a/c + b/d; if equals are divided by non zero equals the quotients are equal.

addition postulate

if a = b and c = d, then a + c = b + d; if equal quantities are added to equal quantities, then the sums are equal.

transitive property

a = a

reflexive property

if a = b, and b = c, then a = c.