Geometry Flashcards

congruent definition

same size and shape ≅

parallel

lines that never intersect; a || b

right angle

measures 90 degrees

perpendicular

lines that meet at a right angle ⊥

collinear

points that lie on the same line

coplanar

objects that lie on the same plane

triangle inequality theorem

the sum of any two sides must be greater than the third; a+b>c

auxillary

any line we make ourselves; dotted

line

any two points determine this

complementary angles

angles with a sum of 90 degrees

supplementary angles

angles that add up to 180 degrees

angle measure format

m∠

how to name angles

∠Vertex if alone, otherwise ∠point-vertex-point.

how to indicate length or distance

AB means the difference between points a and b

point label

letter

line label

AB with a line on top, arrows pointing each way

segment label

BC. line over the letters, no arrows

ray label

BA. endpoint first, line above, arrow pointing ONE direction

intersection

means and; is just what they share. ∩

union

U; means or, EVERYTHING

Things you can assume

colinearity, shape, line=180 degrees

Things you CAN’T assume

right angles, parallel lines, congruence

congruence mark

angles is a curve, lines are hash marks

Addition POE

Adding the same number to both sides of an equation makes an equivalent equation.

Subtraction POE

Subtracting the same number to both sides of an equation makes an equivalent equation.

Division POE

Dividing the same number to both sides of an equation makes an equivalent equation.

Multiplication POE

Multiplying the same number to both sides of an equation makes an equivalent equation.

Reflexive POE

A number is equal to itself

Reflexive POC

A figure is congruent to itself

Symmetric POE

The sides of an equation can be switched

Symmetric POC

The sides of a congruence statement can be switched

Transitive POE

If two numbers are equal to the same number, then they are equal to each other (,)

Transitive POC

If two numbers are congruent to the same number, then they are congruent to each other (,)

Substitution POE

If two numbers are equal, one can replace the other in a congruent statement

Substitution POC

If two figures are congruent, one can replace the other in a congruent statement.

Midpoint

The middle of a segment

Bisector

a line, segment, or ray that divides an object into two equal parts.

Congruent Rule 1

If two angles are right angles, then they are congruent

Congruent Rule 2

If two angles are straight angles, then they are congruent

Proof: Definition of midpoint

If a point is identified as the midpoint of a segment, the two halves of the segment are congruent

Proof: Definition of bisector

If a ray is identified as the bisector of an angle, the two halves of the angle are congruent. If a line is identified as the bisector of a segment, the two halves of the segment are congruent.

AAP: Angle addition postulate

Two adjacent smaller angles make up the larger angle

LPP: Linear Pair Postulate

A linear pair makes a straight angle of 180 degrees

SAP: Segment Addition Postulate

two smaller segments make a larger segment

If angles are supplementary to the same angle, then they are congruent

Supplement rule 1

If angles are supplementary to congruent angles, then they are congruent

Supplement rule 2

If angles are complementary to congruent angles, then they are congruent

Complement rule 1

If angles are complementary to the same angle, then they are congruent

Complement rule 2

VAT

Vertical angles are always congruent