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Chapter 5 Vocabulary
Terms in this set (29)
Triangle Midsegment Theorem
If a segment joins the midpoints of two sides of a triangle, then the segment is parallel to the third side and is half as long
A point, or set of points, that is the same distance from two figures.
PERPENDICULAR Bisector Theorem
If the point is on the perpendicular bisector of a segment, then it is equidistant from endpoints of the segments.
Converse of the PERPENDICULAR Bisector Theorem
If a point is equidistant from the endpoints of a segment, then its on the perpendicular bisector on the segment
ANGLE Bisector Theorem
if a point is on the bisector of an angle then it is equidistant from the two sides of the angle
Converse of the ANGLE Bisector Theorem
If a point in the interior of an angle is equidistant from the sides of the angle, then the point is on the angle bisector.
When three or more lines intersect at one point.
Point of Concurrent
The point where the lines intersect.
Concurrency of PERPENDICULAR Bisectors Theorem
If the perpendicular Bisector of the sides of a triangle are concurrent at a point equidistant from the vertices
Circumcenter of the Triangle
The point of concurrency of the perpendicular bisectors of a triangle.
Since the circumcenter is equidistant from the vertices, you can use the circumcenter as the center of a circle of a circle that contains each vertex of the triangle.
Concurrency of ANGLE Bisectors Theorem
The bisectors of the angles of a triangle are concurrent at a point equidistant form the sides of the triangle.
Incenter of the Triangle
The point of concurrency of the angle bisectors of a triangle.
A circle is inside the triangle with where the center is equidistant from the sides
Median of a triangle
A segment whose endpoints are a vertex and the midpoint of the opposite side.
Centroid of the Triangle (center of gravity for a triangle)
The point of concurrency of the medians.
Concurrency of Medians Theorem
The medians of a triangle are concurrent at a point that is two thirds (2/3) the distance from each vertex to the midpoint of the opposite side
Altitude of a Triangle
is the perpendicular segment from a vertex of the triangle to the line containing the opposite side. an altitude of a triangle can be inside or outside the triangle, or it can be a side of the triangle.
Concurrency of Altitudes Theorem
The lines that contain the altitudes are concurrent.
Orthocenter of a Triangle
The point where the altitudes of a triangle meet.
All possibilities are considered and then all but one are proved false. The remaining possibility must be true.
a proof involving indirect reasoning.
Comparison Property of Inequality
IF a=b+c and c>0, THEN a>b
Corollary to the Triangle Exterior Angle Theorem
The measure of an exterior angle of a triangle is greater than the measure of each of its remote interior angles.
If the 2 sides of a triangle are not congruent, then the larger angle lies opposite the longer side.
If 2 angles of a triangle are not congruent, Then the longer side lies opposite the larger angle.
The sum of the lengths of any 2 sides of a a triangle is greater than the length of the third side.
The Hinge Theorem (SAS Inequality Theorem)
The 2 sides of one triangle are congruent to two sides of another triangle, and the included angles are not congruent, then the longer 3rd side is opposite the larger included angle.
Converse of the Hinge Theorem (SSS Inequality)
If two sides of one triangle are congruent to two sides of another triangle and the third sides are not congruent, then the larger included angle is opposite from the longer third side
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