Math 6-1 to 6-4 test

Circumcenter

Circumcenter

Intersection of perpendicular bisector of side lengths and is equidistant from the vertices. To find, find the line that is perpendicular to line and goes through midpoint.

Incenter

Intersection of the angle bisectors and our equidistant from the sides of the triangle. To find, use formula (ax1 + bx2 +cx3/a+b+c , ay1 + by2 + cy3/a+b+c).

Centroid

Intersection of the medians of a triangle. To find, use formula (x1+x2+x3/3 , y1+y2+y3/3)

Orthocenter

Where the altitudes of the triangle intersect. To find, find line perpendicular to side through the vertex of the altitude and where they intersect.

Median

line segment with endpoints a vertex and midpoint of opposite side.

Altitude

line segment from vertex and perpendicular to opposite side.

comparison property of inequality

a<b, a>b, or a=b

transitive property of inequality

if a<b and b<c, then a<c

if a>b and b>c, then a>c

addition property of inequality

if a>b, then a+c>b+c

if a<b, then a+c<b+c

subtraction property of inequality

if a>b, then a-c>b-c

if a<b, then a-c<b-c

Indirect Proof Steps

First assume that the negation of the conclusion is true. Then, contradict the hypothesis of the original statement. After the contradiction reason indirectly for example since this does not lead to this then the original must be true.

Hinge Theorem

If two sides of a triangle are congruent to two sides of another triangle which ever one has the greatest angle will have the greatest opposite side length.

Converse of Hinge Theorem

If two sides of a triangle are congruent to two sides of another triangle which ever one has the longest third side has the largest angle measure opposite to that side.