Semester 1 Terms

Circumcenter

the point of concurrency of the three perpendicular bisectors of a triangle

Incenter

the point of concurrency of the three angle bisectors of a triangle

Orthocenter

The point of concurrency of the altitudes of a triangle

Centriod

The point of concurrency of the medians of a triangle

The Euler Line

a segment passing through the circumcenter, centroid, and orthocenter of a triangle

Perpendicular Bisector

A line that is perpendicular to a segment at its midpoint.

Angle Bisector

a ray that divides an angle into two congruent angles

altitute

the perpendicular segment from a vertex of the triangle to the line containing the opposite side

Median

a segment whose endpoints are a vertex and the midpoint of the opposite side

concurrent

three or more lines that intersect at one point

center of gravity

Another term for centroid of a triangle

inscribed circle

a circle that is inside the triangle. Made by using the incenter.

circumscribed circle

a circle that is outside the triangle. Made by using the circumcenter.

Incenter Conjecture

The incenter of a triangle is equidistant from the sides of the triangle.

Circumcenter Conjecture

The circumcenter of a triangle is equidistant from the vertices of the triangle.

Angle Bisector Conjecture

If a point is on the bisector of an angle, then it is equidistant from the sides of the angle

compass

A tool used to construct circles and arcs.

protractor

A tool used to measure and draw angles.

Straightedge

a ruler with no markings on it

Ruler

A straight tool used to measure small distances

Triangle Sum Conjecture

The sum of the measures of the angles in every triangle is 180°.

Third Angle Conjecture

If two angles of one triangle are congruent to two angles of another triangle, then the third angles are congruent

Isosceles Triangle Conjecture

If a triangle is isosceles, then its base angles are congruent.

Converse of isosceles triangle conjecture

If two angles in a triangle are congruent, then it is isosceles.

Triangle Inequality Conjecture

The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

Side-Angle Inequality Conjecture

In a triangle, if one side is longer than another side, then the angle opposite the longer side is larger than the angle opposite the shorter side.

Triangle Exterior Angle Conjecture

The measure of an exterior angle of a triangle is equal to the sum of the measures of the non-adjacent interior angles.

SSS Congruence Conjecture (Side-Side-Side)

If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

SAS Congruence Conjecture (Side-Angle-Side)

If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.