HHS9 Geometry Unit 3 Vocabulary

flow proof

A type of proof that uses arrows and boxes to show the flow of a logical argument

paragraph proof

A style of proof in which the statements and reasons are presented in paragraph form.

exterior angle of a polygon

An angle formed by one side of a polygon and the extension of an adjacent side

remote interior angles

the two nonadjacent interior angles corresponding to each exterior angle of a triangle

scalene triangle

a triangle with no congruent sides

isosceles triangle

A triangle with 2 congruent sides

equilateral triangle

a triangle with 3 congruent sides

acute triangle

A triangle with 3 acute angles

right triangle

a triangle with one right angle

obtuse triangle

a triangle with one obtuse angle

Equiangular

all angles are congruent

midsegment of a triangle

a line segment that connects the midpoints of two sides of a triangle

base of isosceles triangle

the third (non-congruent) side of an isoceles triangle

base angles of isosceles triangle

the two angles adjacent to the base

corollary

something that follows once something else has been proven

legs of an isosceles triangle

the two congruent sides of an isosceles triangle

angle bisector

a line, segment, or ray that divides an angle into two congruent angles

perpendicular bisector of a triangle

a line, ray, or segment that is perpendicular to a side of the triangle at the midpoint of the side

congruent polygons

two polygons whose corresponding sides and angles are congruent

included angle

the angle formed by two adjacent sides of a polygon

included side

the side located between two consecutive angles of a polygon

interior angles

the angles between adjacent sides of a figure

hypotenuse

the side of a right triangle opposite the right angle

legs of a right triangle

the two sides that form the right angle

circumcenter of a triangle

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

incenter of a triangle

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

circumscribed about

A circle is circumscribed about a polygon if the vertices of the polygon are on the circle.

concurrent

happening at the same time

inscribed in

A circle is inscribed in a polygon if the sides of the polygon are tangent to the circle.

point of concurrency

the point where concurrent lines intersect

altitude of a triangle

the perpendicular segment from a vertex to the opposite side or to the line that contains the opposite side

centroid of a triangle

the point of concurrency of the three medians of a triangle

median of a triangle

a segment from a vertex to the midpoint of the opposite side

orthocenter of a triangle

the point of concurrency of the three altitudes of a triangle

Triangle Exterior Angle Theorem

The measure of an exterior angle is equal to the sum of the two remote interior angles.

Parallel Postulate

If there is a line and a point not on the line, then there is exactly one line through the point parallel to the given line.

Triangle Sum Theorem

The sum of the measures of the interior angles of a triangle is 180 degrees

Triangle Midsegment Theorem

A midsegment of a triangle is parallel to a side of the triangle, and its length is half the length of that side

Base Angles Theorem

if 2 sides of a triangle are congruent, then the angles opposite them are congruent

Converse of the Base Angles Theorem

If two angles of a triangle are congruent, then the sides opposite them are congruent.

Third Angles Theorem

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

Side-Side-Side (SSS)

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

Side-Angle-Side (SAS)

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.

Angle-Side-Angle (ASA)

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

Angle-Angle-Side (AAS)

If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of a second triangle, then the two triangles are congruent.

Hypotenuse Leg (HL)

If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent.

Corresponding Parts of Congruent Triangles are Congruent (CPCTC)

If two triangles are congruent, then all sets of corresponding parts are also congruent.

Concurrency of Medians Theorem

The medians of a triangle are concurrent and the point of concurrence, the centroid, is one-third of the distance from the opposite side to the vertex along the median.

Hinge Theorem

If two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second, then the third side of the first is longer than the third side of the second.

Converse of the Hinge Theorem

If two sides of one triangle are congruent to two sides of another triangle, and the third side of the first is longer than the third side of the second, then the included angle of the first is larger than the included angle of the second.

Triangle Angle Sum Theorem

The sum of the measures of the angles of a triangle is 180.

Isosceles Triangle Theorem

If two sides of a triangle are congruent, then the angles opposite those sides are congruent.

Converse of the Isosceles Triangle Theorem

If two angles of a triangle are congruent, then the sides opposite those angles are congruent.

Corollary to Isosceles Triangle Theorem

If a triangle is equilateral, then the triangle is equiangular

Corollary to the Converse of the Isosceles Triangle Theorem

If a triangle is equiangular, then it is also equilateral

Concurrency of Perpendicular Bisectors Theorem

The perpendicular bisectors of a triangle intersect at a point that is equidistant from the vertices of the triangle

Concurrency of Angle Bisectors Theorem

The angle bisectors of a triangle intersect at a point that is equidistant from the sides of the triangle.

vertex angle of an isosceles triangle

The angle formed by the legs of an isosceles triangle.