Geometry Vocab

Unit 1

(keep going to learn vocab words from Unit 1)

point

a location in space with no definite size or dimension

line

a straight path that extends infinitely in both directions with no thickness or endpoints

collinear points

points that lie on the same straight line

segment

part of a line with two endpoints

ray

part of a line with one endpoint and extending infinitely in one direction

vertical angles

two nonadjacent angles formed by intersecting lines that are congruent

linear pair

two adjacent angles whose noncommon sides form a straight line

parallel lines

lines in the same plane that never intersect

perpendicular lines

lines that intersect to form right angles

skew lines

noncoplanar lines that do not intersect and are not parallel

plane (face)

a flat surface that extends infinitely in all directions

coplanar

points or lines that lie on the same plane

angle

a figure formed by two rays with the same endpoint

vertex

the common endpoint of the sides of an angle

legs

the sides that form an angle or triangle other than the base

interior of angle

the region inside the rays of an angle

exterior of angle

the region outside the rays of an angle

acute angle

an angle that measures greater than 0° and less than 90°

obtuse angle

an angle that measures greater than 90° and less than 180°

right angle

an angle that measures exactly 90°

straight angle

an angle that measures exactly 180°

reflex angle

an angle that measures greater than 180° and less than 360°

supplementary angles

two angles whose measures add up to 180°

transversal

a line that intersects two or more other lines in a plane at different points

corresponding angles

angles in matching positions when a transversal crosses two lines

alternate interior angles

nonadjacent interior angles on opposite sides of a transversal

consecutive interior angles

interior angles on the same side of a transversal

corresponding angles theorem

if a transversal intersects parallel lines, then corresponding angles are congruent

consecutive interior angles theorem

if a transversal intersects parallel lines, then consecutive interior angles are supplementary

alternate interior angles theorem

if a transversal intersects parallel lines, then alternate interior angles are congruent

converse of the corresponding angles theorem

if two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel

converse of the alternate interior angle theorem

if two lines are cut by a transversal so that alternate interior angles are congruent, then the lines are parallel

converse of the consecutive interior angles theorem

if two lines are cut by a transversal so that consecutive interior angles are supplementary, then the lines are parallel

Unit 2

(keep going to learn vocab words from Unit 2)

reflexive property

any geometric figure is congruent to itself, and any quantity is equal to itself.

symmetric property

if one figure is congruent to another, then the second is congruent to the first (if a=b, then b=a)

transitive property

if one figure is congruent to a second and the second is congruent to a third, then the first is congruent to the third (if a=b and b=c, then a=c).

distribution property

multiplying a number by a sum is the same as multiplying each term in the sum and then adding the results (a(b + c) = ab + ac).

substitution property

if two quantities are equal, one can be substituted for the other in any equation or expression (if a = b, then b can replace a in any expression).

addition property of equality

if the same number is added to both sides of an equation, the equality remains true (if a = b then a + c = b + c).

subtraction property of equality

if the same number is subtracted from both sides of an equation, the equality remains true (if a = b then a − c = b − c).

multiplication property of equality

if both sides of an equation are multiplied by the same number, the equality remains true (if a = b then ac = bc).

division property of equality

if both sides of an equation are divided by the same number, the equality remains true (if a = b, then a ÷ c = b ÷ c).

partition property

the whole is equal to the sum of its parts.

adjacent angles

two angles that share a common vertex and a common side but don’t overlap.

complementary angles

two angles are complementary if their measures add up to 90 degrees.

congruent supplements theorem

if two angles are supplementary to the same angle or congruent angle, then they’re congruent.

vertical angles theorem

vertical angles are congruent.

congruent complements theorem

if two angles are complementary to the same angle or congruent angle, then they’re congruent.

lines perpendicular to a transversal theorem

if two lines are perpendicular to the same transversal, then the lines are parallel.

perpendicular transversal theorem

if a line is perpendicular to one of two parallel lines, then it’s perpendicular to the other as well.

Unit 3

(keep going to learn vocab words from Unit 3)

interior angles

the angles inside a polygon formed by its sides.

exterior angles

the angles formed outside a polygon when one side is extended.

triangle inequality theorem

the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

triangle angle sum theorem

the sum of the interior angles of a triangle is always 180 degrees.

exterior angle theorem

the measure of an exterior angle of a triangle equals the sum of the two nonadjacent interior angles.

scalene triangle

a triangle with no congruent sides.

isosceles triangle

a triangle with two congruent sides.

equilateral triangle

a triangle with all sides congruent.

acute triangle

a triangle with all angles less than 90 degrees.

right triangle

a triangle with one 90-degree angle.

obtuse triangle

a triangle with one angle greater than 90 degrees.

isosceles triangle theorem

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

converse of isosceles triangle theorem

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

midpoint

a point that divides a segment into two congruent parts.

segment bisector

a line, ray, or segment that passes through the midpoint of another segment.

angle bisector

a ray that divides an angle into two congruent angles.

corresponding parts of congruent triangles (polygons) congruent (CPCTC)

if two triangles (or polygons) are congruent, then all their corresponding sides and angles are congruent.

side-side-side congruence postulate (SSS)

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

side-angle-side congruence postulate (SAS)

if two sides and the included angle of one triangle are congruent to two sides and the included angle of another, the triangles are congruent.

angle-side-angle congruence postulate (ASA)

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

angle-angle-side congruence postulate (AAS)

if two angles and a non-included side of one triangle are congruent to the corresponding parts of another, the triangles are congruent.

hypotenuse-leg congruence postulate (HL)

in right triangles, if the hypotenuse and one leg of one triangle are congruent to the corresponding parts of another, the triangles are congruent.

Unit 4

(keep going to learn vocab words from Unit 4)

similar polygons

polygons that have the same shape but not necessarily the same size, with corresponding angles congruent and corresponding sides proportional.

scale factor

the ratio of the lengths of corresponding sides of two similar polygons.

angle-angle similarity (AA~)

when two triangles have two pairs of corresponding angles congruent, the triangles are similar.

side-side-side similarity (SSS~)

when the three pairs of corresponding sides of two triangles are proportional, the triangles are similar.

side-angle-side similarity (SAS~)

when two sides of one triangle are proportional to two sides of another triangle and the included angles are congruent, the triangles are similar.

geometric mean

a value that is the square root of the product of two numbers.

altitude

a line segment drawn from a vertex of a polygon that is perpendicular to the opposite side or the line containing the opposite side.

altitude-hypotenuse theorem

in a right triangle, the altitude to the hypotenuse creates two smaller right triangles that are similar to the original triangle and to each other.

altitude rule

the length of the altitude to the hypotenuse of a right triangle is the geometric mean of the two segments of the hypotenuse.

leg rule

in a right triangle, each leg is the geometric mean of the entire hypotenuse and the segment of the hypotenuse adjacent to that leg.

triangle proportionality theorem

if a line is parallel to one side of a triangle and intersects the other two sides, it divides those sides proportionally.

midsegment theorem

the segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half its length.

proportional parts with parallel lines

segments between parallel lines are proportional to other segments between the same lines, and triangles formed by parallel lines are similar.

special segments of similar triangles

certain lines like altitudes, medians, and angle bisectors in similar triangles are proportional to corresponding sides.

triangle angle bisector theorem

an angle bisector in a triangle divides the opposite side into segments that are proportional to the other two sides of the triangle.

median

a segment that connects a vertex of a triangle to the midpoint of the opposite side.

Unit 5

(keep going to learn words from unit 5)

hypotenuse

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

leg

either of the two sides that form the right angle in a right triangle

pythagorean theorem

a rule that states the square of the hypotenuse equals the sum of the squares of the two legs

pythagorean triple

a set of three whole numbers that can represent the side lengths of a right triangle because they satisfy the pythagorean theorem

pythagorean theorem - classifying right

when the square of the longest side equals the sum of the squares of the other two sides, the triangle is right

pythagorean theorem - classifying acute

if the sum of the squares of the other two sides is greater than the longest side, then the triangle is acute

pythagorean theorem - classifying obtuse

if the sum of the squares of the other two sides is less than the longest side, then the triangle is obtuse