Theorem, Postulate, Corollary List

Front 1

Line Postulate

Back 1

There is EXACTLY ONE line that passes through / connects any 2 points

Front 2

Plane Postulate

Back 2

There is EXACTLY ONE plane connecting / containing 3 noncollinear points

Front 3

Linear

Back 3

Extending along a STRAIGHT line

Front 4

Collinear

Back 4

2 or MORE points lying in the SAME STRAIGHT line

Front 5

Noncollinear

Back 5

NOT lying on the SAME STRAIGHT line

Front 6

Flat Plane Postulate

Back 6

If there are 2 points on a plane, then the line that connects these points are also on that same plane

Front 7

Midpoint Theorem

Back 7

If a line is divided into 2 at its midpoint, that means the 2 line segments are congruent

Front 8

Ruler Postulate

Back 8

You can measure any line or line segment given any 2 points from that line

Hint 8

Front 9

Segment Addition Postulate

Back 9

If you have a collinear line with 3 points A, B, C, then line AB + BC = AC

If AB + BC = AC, that means B lies in between A and C

Hint 9

Front 10

Reflexive Property

Back 10

AB ≅ AB; compare it to itself

Front 11

Symmetric Property

Back 11

If AB ≅ CD, then CD ≅ AB; comparing 2 congruent items

Front 12

Transitive Property

Back 12

If AB ≅ CD, and CD ≅ EF, then AB ≅ EF; comparing 3 or more congruent items

Front 13

Protractor Postulate

Back 13

You can measure any angle given the 2 rays that form that angle

Hint 13

Front 14

Adjacent

Back 14

They share the same side or they're next to each other

Front 15

Supplement theorem

Back 15

If you merge 2 angles and they form 180°, they are supplementary

Hint 15

Front 16

Complement theorem

Back 16

If you merge 2 angles and they form 90°, they are complementary

Hint 16

Front 17

Vertical Angle Theorem

Back 17

Vertical angles are always congruent

Hint 17

Front 18

Perpendicular

Back 18

When 2 lines connect to form 90°

Front 19

Right Angle Theorems

Back 19

Front 20

Corresponding Angles Postulate

Back 20

Note that the 2 lines have to be PARALLEL

Front 21

Alternate Interior Angles Theorem

Back 21

If you have 2 parallel lines cut by a transversal, the alternating angles INSIDE the 2 parallel lines are congruent (4≅5, 3≅6)

Front 22

Consecutive Interior Angles Theorem

Back 22

If you have 2 parallel lines cut by a transversal, the angles INSIDE the 2 parallel lines that are also on the same side of the transversal are supplementary (4+6=180°, 3+5=180°)

Front 23

Alternate Exterior Angles Theorem

Back 23

If you have 2 parallel lines cut by a transversal, the alternating angles OUTSIDE the 2 parallel lines are congruent (1≅8, 2≅7)

Front 24

Perpendicular Transversal Theorem

Back 24

If a transversal line cuts through 2 parallel lines and it is perpendicular to one of them, then it is perpendicular to both lines

Hint 24

Front 25

Parallel Postulate

Back 25

If you have a line and a random point that's not touching the line, there is EXACTLY ONE line that can go through that point and still be parallel to the first line

Front 26

Proving Lines Parallel Theorems

Back 26

Just familiarize yourself with these. It'll just help you prove that 2 lines are parallel

Front 27

Angle Sum Theorem

Back 27

The sum of the angles of a triangle is always 180°

Hint 27

Front 28

Third Angle Theorem

Back 28

If 2 angles of a triangle are congruent to 2 angles of another triangle, then the 3rd angles of both triangles are congruent

Front 29

Exterior Angle Theorem

Back 29

If you extend one side of a triangle, the angle outside the triangle is equal to the combination of the 2 angles inside the triangle that aren't touching the exterior angle

Hint 29

Front 30

If you have a right triangle, the sum of the 2 acute angles will always be ___.

Back 30

90°

Front 31

Side-Side-Side Congruence (SSS) Postulate

Back 31

Two triangles are congruent if the 3 sides of both triangles are congruent

Hint 31

Front 32

Side-Angle-Side Congruence (SAS) Postulate

Back 32

Two triangles are congruent if the 2 sides of both triangles and the angle BETWEEN both sides are congruent

Hint 32

Front 33

Angle-Side-Angle Congruence (ASA) Postulate

Back 33

Two triangles are congruent if the 2 angles of both triangles and the side BETWEEN both sides are congruent

Front 34

Right Triangle Congruence

Back 34

Just remember that the HYPOTENUSE is the longest side (the side that doesn't touch the right angle) and the other sides are LEGS

Front 35

Isosceles Triangle Theorem

Back 35

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

FOCUS IS ON THE SIDES BEING CONGRUENT

Hint 35

Front 36

Converse of Isosceles Triangle Theorem

Back 36

If 2 angles of a triangle are congruent, then the 2 sides opposite them are also congruent FOCUS IS ON THE ANGLES BEING CONGRUENT