Download Unit 4

Geometry Unit 4 Vocabulary
Triangles
Acute Angle – an angle that measures between 0o and 90o.
Acute Triangle – a triangle made up of 3 acute angles.
Altitude - A line segment extending from any vertex of a triangle perpendicular to the line containing the
opposite side
Angle Bisector– A ray whose endpoint is the vertex of the angle and which divides the angle into two congruent
angles
CAB  DAB
Base of an Isosceles Triangle– The side that is not a leg. That is, the non-congruent side of the triangle.
Base Angle of an Isosceles Triangle– the angles formed by the congruent legs and the base of the triangle
Bisect – to cut something exactly in half, or into two equal pieces
Centroid – the point where the three medians of the triangle meet. It is also called the center of gravity of the
triangle.
 x1  x 2  x3 y1  y 2  y3 
,


3
3


Circumcenter – the point of concurrency of the three perpendicular bisectors of each side of the triangle. It is
may be located inside, outside or on the triangle. It is equidistant from each vertex of the triangle.
It is used to circumscribe a circle about a triangle.
Circumscribed - a geometric figure that is drawn around another geometric figure so as to touch all its vertices
Circle is circumscribed around a triangle.
Concurrent - when three or more lines meet at a single point. In a triangle, the three medians, three
perpendicular bisectors, three angle bisectors, and three altitudes are each concurrent.
Equilateral Triangle – a triangle with three sides of the same length. Note: All angles in an equilateral triangle
measure 60o.
Exterior angle of a polygon– an angle that forms a linear pair with an angle of a polygon.
Hypotenuse – the side of a right triangle opposite the right angle; the longest side of a right triangle
Incenter – the point where three angle bisectors meet The incenter is equidistant from all three sides of a
triangl). It is always on the inside of a triangle.
It is used to inscribe a circle in a triangle.
Inscribe- drawing one shape inside another with it touching each side
Point O is the incenter, the intersection of angle bisectors.
Isosceles Triangle – a triangle with two sides of the same length. Note: there is a theorem that states the base
angles are also equal.
Legs of an Isosceles Triangle – The two congruent sides of an isosceles triangle.
Median (of a triangle) - A line segment extending from any vertex of a triangle to the midpointof the opposite
side
Obtuse Angle – an angle that measures between 90o and 180o.
Obtuse Triangle– a triangle that has one obtuse angle.
Right Angle – an angle that measures exactly 90o. It is indicated by a little square box.
Right Triangle– a triangle that has one right angle.
Scalene Triangle– a triangle with all sides a different length.
Vertex – the point where two segments or rays meet to form an angle. (plural is vertices)
Vertex angle of an Isosceles Triangle – In an isosceles triangle, the angle formed by the two legs of equal
length. The vertex angle is always opposite the base.
Postulate/Axioms/Theorems/Corollaries
Isosceles Triangle Altitude Theorems


The altitude to the base of an isosceles triangle bisects the vertex angle.
The altitude to the base of an isosceles triangle bisects the base
Isosceles Triangle Converse Theorem – If two angles of a triangle are congruent, the sides opposite them are
congruent.
Isosceles Triangle Theorem – If two sides of a triangle are congruent, the angles opposite them are congruent.
Sum of Interior Angles of a Triangle Theorem – the sum of the interior angles of a triangle is 180o
Triangle Exterior Angle Theorem – the measure of an exterior angle is equal to the sum of the measures of the
two non-adjacent interior angles.
Triangle Inequality Theorem – The sum of the lengths of any two sides of a triangle must be greater than the
third side.