Download Theorems you should know!! Below is a list of MOST of the

Theorems you should know!!
Below is a list of MOST of the Theorems we have learned thus far. You need to understand and know
how to apply these theorems. For each Theorem listed below, fill in the blank with the appropriate
terminology.. You must also draw a diagram next to each one to illustrate what the theorem listed is
actually saying.
1. Segment Addition Postulate
If B is between A and C, then ________________________.
2. Angle Addition Postulate
If S is in the interior of  PQR, then, ____________________________________________.
3. Pythagorean Theorem
In a right triangle, the _________ of the ______________ of the lengths of the legs is equal to the
_______________ of the length of the ______________________.
4. Linear Pair Theorem
If two angles are supplementary, then they are ________________________________.
5. Vertical Angles Theorem
Vertical angles are _____________________.
6. Corresponding Angles Postulate
If two _________________ lines are cut by a _______________________, then the pairs of
corresponding angles are __________________________.
7. Alternate Interior Angles Theorem
If two __________________ lines are cut by a _______________________, then the pairs of alternate
interior angles are __________________________.
8. Alternate Exterior Angles Theorem
If two _________________ lines are cut by a ________________________, then the pairs of alternate
exterior angles are _________________________.
9. Same-Side Interior Angles Theorem
If two _______________ lines are cut by a ___________________________, then the pairs of sameside interior angles are ______________________________.
10. Parallel Lines Theorem
In a coordinate plane, two lines are parallel if and only if _______________________________.
11. Perpendicular Lines Theorem
In a coordinate plane, two lines are perpendicular if and only if ___________________________
____________________________________________________________. Vertical and horizontal lines
are always _____________________________.
12. Triangle Sum Theorem
The __________ of the ______________ measures of a triangle is ______________.
The acute angles of a right triangle are ___________________________________.
The measure of each angle of an equiangular triangle is ___________.
13. Exterior Angle Theorem
The measure of an __________________ angle of a triangle is equal to the __________ of the measures
of its _____________________________________________.
14. Third Angles Theorem
If two angles of one triangle are congruent to two angles of another triangle, then ____________
_________________________________________________________________________.
15. Triangle Congruence Theorems
List the “shortcuts” for all of the theorems that can be used to prove triangle congruence.
_______________________________________________________.
16. Isosceles Triangle Theorem (and it’s Converse)
If two sides of a triangle are congruent, then _______________________________________
____________________________________________________________.
If two angles of a triangle are congruent, then ______________________________________
____________________________________________________________.
If a triangle is equilateral, then it is _________________________________.
If a triangle is equiangular, then it is _________________________________.
17. Triangle Midsegment Theorem
A midsegment of a triangle is ______________________ to a side of the triangle, and it’s
___________________ is ________________ the length of that side.
18. Triangle Inequality Theorem
The _____________ of any two sides of a triangle must be ____________________________
___________________________________________________________________.
19. Pythagorean Inequalities Theorem
In  ABC, c is the length of the longest side. If __________________________, then  ABC is an obtuse
triangle. If _____________________________, then  ABC is an acute triangle.
20. 45° -45° – 90° Triangle Theorem
In a 45 – 45 – 90 triangle, both legs are ________________________, and the length of the hypotenuse is
the length of the leg times ___________.
21. 30° – 60° – 90° Triangle Theorem
In a 30 – 60 – 90 triangle, the length of the hypotenuse is ________ times the length of
________________________________, and the length of the longer leg is the length of the shorter leg
times __________.
Vocabulary You Should Know!
Coplanar
Collinear
Ray
Opposite Rays
Midpoint
Bisect
Segment Bisector
Acute
Right
Obtuse
Angle Bisector
Congruent
Adjacent Angles
Linear Pair
Complementary
Supplementary
Vertical Angles
Hypotenuse
Conjecture
Counterexample
Inductive Reasoning
Deductive Reasoning
Conditional Statement
Converse
Inverse
Contrapositive
Alternate Exterior Angles
Alternate Interior Angles
Corresponding Angles
Distance From a Point To A Line
Parallel Lines
Perpendicular Bisector
Skew Lines
Transversal
Same – Side Interior Angles
Corresponding Angles / Sides
Median
Equiangular
Equilateral
Scalene Triangle
Vertex Angle
Remote Interior Angle
Obtuse Triangle
Isosceles Triangle
Altitude
Pythagorean Triple
Midsegment of a Triangle
Formulas You Should Be Familiar With!
Slope Formula:
y2  y1
x2  x1
Distance Formula:
Midpoint Formula:
 x1  x2 y1  y2 
,


2 
 2
x2  x1 2  y2  y1 2
Slope – Intercept Form of a Line:
y  mx  b
Point – Slope Form of a Line:
y  y1  mx  x1 
30 – 60 – 90 Triangles:
45 – 45 – 90 Triangles:
x , x 3 , 2x
x, x,x 2