Geometry Vocab

Two angles that add up to exactly 90°

Two angles that add to exactly 180°

A location that has no sides

Represented by a lettered dot (i.e. P, Q, etc.)

An infinite number of points on a straight path that extends in two directions with no end and no thickness

An infinite number of points and lines on a flat surface that extends forever without end and has no thickness

Part of a line that consists of two endpoints and all of the points between them

Part of a line that consists of one endpoint and all the points in one direction from the endpoint to infinity

Rays with the same endpoint that lie on the same line

Formed by two rays with the same endpoint. Each ray is a side of the angle. The endpoint is the vertex.

Lines that intersect to form a right angle

⟂ Symbol (i.e. AB ⟂ CD)

Lines that lie in the same plane and do not intersect

∥ or // Symbol (i.e. AB ∥ CD)

∠ Symbol (i.e. ∠ABC or ∠CBA)

Lines that do not lie in the same plane and do not intersect

Points that lie on the same line

Points that lie on the same plane

A statement that is assumed to be true

Every point on a line can be paired with a unique real number. The number is called the coordinate of the point

If points A, B and C are on the same line, with B being between A and C, then AB + BC = AC

The measure of an angle is the absolute value of the difference of the real numbers paired with the sides of the angle

Equal in value/measure

≅ Symbol (i.e. AB ≅ CD)

Geometric figure made using only a compass and a straight edge

A line, segment or ray that is perpendicular to another segment amd splits the segment into two congruent segments

A ray that divides an angle into two congruent angles

The middle point of a segment

A type of reasoning that reaches conclusions based on an observation of specific data or past events

An unproven statementule based on inductive reasoning

An example that shows a statement/conjecture is false

An if-then statement (i.e. IF Alberto washes the car, THEN he can go to the movies). Contains a hypothesis and a conclusion.

The part of a conditional after “if”

The part of a conditional after “then”

Conditional notation

Tells if a statement is true or false

Flips the hypothesis and conclusion in a conditional

Has the opposite meaning of the original statement

~ symbol

Negates the hypothesis and the conclusion in a conditional

Inverse conditional symbol

Negates and flips both the hypothesis and the conclusion in a conditional

Combination of a conditional and a converse (i.e. I did my chores if and only if I get my allowance.

Biconditional symbolic notation

A process of reasoning using given and previously known facts to reach a logical conclusion

If a conditional and its hypothesis are true, then its conclusion is also true.

A law of logic that states that given two true conditionals with the conclusion of the first being the hypothesis of the second, there exists a third true conditional having the hypothesis of the first and the conclusion of the second (TLDR if p→q and q→r, then p→r is true)

Doing something to both sides of an equality

a(b+c)=ab+ac

If a=b, then a may be substituted by b in any expression or equation

A value will always equal itself.

If a=b, then b=a

If a=b, and a=c, then a=c

Two angles that form a line or straight angle

The sum of the measures of a linear pair is 180°

Vertical angles are congruent

If two angles are supplementary to congruent angles, then they are congruent to each other.

If two angles are complementary to congruent angles, then they are congruent to each other.

All right angles are congruent

If two angles are supplementary and congruent, then each angle is a right angle.

A line that intersects two or more lines at distinct points.

Nonadjacent angles that lie on the same side of the transversal and in corresponding positions.

Nonadjacent angles that are on the opposide side of the transversal and on the exterior of the two lines.

Nonadjacent angles that are on the opposide side of the transversal and on the interior of the two lines.

Nonadjacent angles that are on the same side of the transversal and on the exterior of the two lines.

Nonadjacent angles that are on the same side of the transversal and on the interior of the two lines.

If a transversal intersects two parallel lines, then same side interior angles are supplementary

If a transversal intersects two parallel lines, then same side exterior angles are supplementary.

If a transversal intersects two parallel lines, then alternate interior angles are congruent.

If a transversal intersects two parallel lines, then alternate exterior angles are congruent.

If a transversal intersects two parallel lines, then corresponding angles are congruent.