Unit 4 Vocabulary

Right Triangle

• A triangle with one 90-degree angle.

• A triangle with all sides equal.

• A triangle with two equal angles.

• A triangle with no equal sides.

Centroid

• The point of concurrency of the medians of a triangle.

• The longest side of a triangle.

• The angle bisector of a triangle.

• The midpoint of the hypotenuse of a right triangle.

Scalene Triangle

• A triangle with all sides of equal lengths.

• A triangle with two sides of equal lengths.

• A triangle with all sides of different lengths.

• A triangle with one angle greater than 90 degrees.

Corollary to a Theorem

• A statement that follows readily from a previous theorem.

• A theorem that contradicts another theorem.

• An assumption made without proof.

• A statement that is always true regardless of conditions.

Converse of the Perpendicular Bisector Theorem

• If a point is equidistant from the endpoints of a segment, it lies on the perpendicular bisector of the segment.

• If a point lies on the perpendicular bisector of a segment, it is equidistant from the endpoints of the segment.

• If a point is not equidistant from the endpoints of a segment, it lies on the perpendicular bisector of the segment.

• If a point lies on the segment, it is equidistant from the endpoints of the segment.

Equiangular Triangle

• A triangle where all angles are equal.

• A triangle with one right angle.

• A triangle with all sides of different lengths.

• A triangle where the sum of angles is 180 degrees.

Altitude

• A line segment from the midpoint of one side to the opposite vertex.

• A perpendicular segment from a vertex to the line containing the opposite side.

• The longest side of a triangle opposite the largest angle.

• A line that bisects an angle of a triangle.

Converse of the Angle Bisector Theorem

• If a point is equidistant from the sides of an angle, it lies on the bisector of the angle.

• If a point lies on the bisector of an angle, it is equidistant from the sides of the angle.

• If a point is outside the angle, it cannot be equidistant from the sides.

• If a point is equidistant from the vertex of an angle, it lies on the angle bisector.

Exterior Angle

• an angle that forms a linear pair with one of the interior angles (by extending the side of the polygon)

• an angle that is formed by two adjacent sides of a polygon

• an angle that is opposite to an interior angle of a polygon

• an angle that measures more than 180 degrees

Circumcenter

• The point of concurrency of the perpendicular bisectors of a triangle.

• The center of a circle that passes through all vertices of a triangle.

• The point where the altitudes of a triangle intersect.

• The midpoint of the longest side of a triangle.