Geometry Vocab | Midterm

midsegment of a triangle

a segment that joins the midpoints of 2 sides of a triangle

perpendicular bisector of a triangle

a line that cuts one of the triangle's sides exactly in half (bisects it) and forms a 90-degree angle (is perpendicular to it) at that midpoint, not necessarily passing through a vertex

angle bisector of a triangle

A line segment that bisects any angle of the triangle and terminates in the side opposite that angle

median of a triangle

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

altitude of a triangle

a segment that connects a vertex of a triangle to the opposite side so that it is perpendicular to that side

circumcenter of a triangle

the point at which the three perpendicular bisectors intersect in a triangle

incenter of a triangle

the point at which the three angle bisectors intersect in a triangle

centroid of a triangle

the point at which the three medians intersect in a triangle

orthocenter of a triangle

the point at which the three altitudes intersect in a triangle

Triangle Midsegment Theorem

If a segment joins the midpoints of two sides of a triangle

Perpendicular Bisector Theorem

If a point is on the perpendicular bisector of a segment

Angle Bisector Theorem

If a point is on the bisector of an angle

Pythagorean Theorem

a²+b²=c²

Triangle Inequality Theorem

The sum of the lengths of the 2 smaller sides of a triangle is greater than the length of the third side.

Collinear points

a set of points that lie on the same line

Coplanar

points in the same plane.

Line segment

part of a line with two endpoints

Opposite rays

two rays that share an endpoint and extend in opposite directions to form a line

Midpoint

point that divides a segment into two congruent segments

Midpoint formula

a formula used to find the midpoint between two endpoints

Segment bisector

any point, line, ray, or plane that cuts a line segment into two perfectly equal halves, always passing through the segment's midpoint

Obtuse angle

angle that measures greater than 90 degrees and less than 180 degrees

Acute angle

angle that measures less than 90 degrees

Right angle

angle that measures exactly 90 degrees

Angle bisector

a ray that divides an angle into two congruent angles

Congruent segments

segments having the same measure

Bisect

to divide into two equal parts

Point

an exact location in space; it has neither shape nor size.

Line

made up of points and has no thickness or width

Plane

a flat surface made up of points that extends infinitely in all directions

Intersection

the set of points that figures have in common

Space

a boundless area

Distance formula

a formula for computing the distance between two points in a coordinate plane

Ray

a part of a line that starts at an endpoint and extends forever in one direction

Angle

a figure formed by two rays with a common endpoint called the vertex

Vertex

the common endpoint of an angle - where the sides intersect

Adjacent angles

two angles that share a common side and have the same vertex - "next to" each other

Complementary angles

two angles whose measures have a sum of 90 degrees

Linear pair

adjacent angles that are supplementary -combined

Supplementary angles

two angles whose measures have a sum of 180 degrees

Straight angle

an angle that measures 180 degrees

Congruent angles

angles that have the same measure

Vertical angles

two nonadjacent angles formed by two intersecting lines - "across from" each other always congruent

Angle Addition Postulate

if point B lies in the interior of <AOC then m<AOB+m<BOC=m<AOC

Perpendicular

intersecting at or forming right angles

Segment Addition Postulate

If B is between A and C

Perpendicular bisector

a line (or ray/segment) that cuts another line segment exactly in half (bisects) and forms a 90-degree (right) angle at the point of intersection (perpendicular)

Parallel lines

lines in the same plane that never intersect

consecutive (same side) interior angles

interior angles that are on the same side of the transversal

alternate interior angles

pairs of angles on opposite sides of a transversal (a line cutting across two others) and between those two lines

alternate exterior angles

pairs of angles on opposite sides of a transversal line and outside the two lines it intersects

corresponding angles

angles on the same side of the transversal and in the same position

consecutive (same side) exterior angles

exterior angles that are on the same side of the transversal

transversal

a line that intersects two or more lines

parallel lines

lines in the same plane that never intersect

skew lines

non-coplanar lines that do not intersect

triangle

3 sided polygon

The sum of the measures of the interior angles of a triangle

180 degrees

ASA

Two triangles are congruent if 2 sets of corresponding angles and their included side are congruent.

SAS

Two triangles are congruent if 2 sets of corresponding sides and their included angles are congruent.

AAS

Two triangles are congruent if two angles and the side opposite one of them are congruent.

SSS

Two triangles are congruent if all 3 sets of corresponding sides are congruent.

scalene triangle

a triangle with no equal sides

equilateral triangle

a triangle with three congruent sides

isosceles triangle

a triangle that has 2 equal sides.

acute triangle

a triangle with 3 acute angles

obtuse triangle

a triangle with one obtuse angle

right triangle

a triangle with one right angle

hypotenuse

the side of a right triangle opposite the right angle and the longest side of a right triangle

interior angle of a triangle

an angle inside the triangle

exterior angle of a triangle

an angle formed by one side of a triangle and the extension of another side

Hypotenuse-Leg Postulate

If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and corresponding leg of another right triangle

congruent triangles

triangles whose corresponding angles and sides are congruent. (They are exactly the same size and shape.)

Congruency Statement

Statement that tells which parts in one triangle correspond to the parts in the other triangle

CPCTC

corresponding parts of congruent triangles are congruent

Exterior Angle Theorem

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles.

Triangle Angle Sum Theorem

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