Geometry Proof Packet
Keep in your binder
Solving the Mystery of the Proof
Suppose you need to solve a crime mystery. You survey the crime scene, gather the facts, and
write them down in your memo pad. To solve the crime, you take the known facts and, step by
step, show who committed the crime. You conscientiously provide supporting evidence for each
statement you make.
Amazingly, this is the same process you use to solve a proof. The following steps will take you
through the whole process.
1. State the given.
The given is the hypothesis and contains all the facts that are provided. The given is the
information with which you are provided in order to complete the proof. The given is generally
written in geometric shorthand in an area above the proof.
2. Get or create a drawing that represents the given.
They say a picture is worth a thousand words. You don't exactly need a thousand words, but you
do need a good picture. When you come across a geometric proof, if the artwork isn't provided,
you're going to have to provide your own. Look at all the information that's provided and draw a
figure. Make it large enough that it's easy on the eyes and that it allows you to put in all the
detailed information. Be sure to label all the points with the appropriate letters. If lines are
parallel, or if angles are congruent, include those markings, too.
3. State what you're going to prove.
The last line in the statements column of each proof matches the prove statement. The prove
statement is where you state what you are trying to show is true. Like the given, the prove
statement is also written in geometric shorthand in an area above the proof. It references parts in
your figure, so be sure to include the information from the prove statement in your figure.
4. Provide the proof itself.
The proof is a series of logically deduced statements — a step-by-step list that takes you from
the given; through definitions, postulates, and previously proven theorems; to the prove
statement.
Remember the following:



The given is not necessarily the first information you put into a proof. The given info
goes wherever it makes the most sense. That is, it may also make sense to put it into the
proof in an order other than the first successive steps of the proof.
The proof itself looks like a big letter T. The T makes two columns. You put a
Statements label over the left column and a Reasons label over the right column.

Think of proofs like a game. The object of the proof game is to have all the statements in
your chain linked so that one fact leads to another until you reach the prove statement.
However, before you start playing the proof game, you should survey the playing field
(your figure), look over the given and the prove parts, and develop a plan on how to win
the game. Once you decide on your strategy, you can proceed statement by statement,
carefully documenting your every move in successively numbered steps. Statements
made on the left are numbered and correspond to similarly numbered reasons on the
right. All statements you make must refer back to your figure and previous statements
then finally end with the prove statement. The last line under the Statements column
should be exactly what you wanted to prove.

Statements and their corresponding reasons must begin on the same line.

Reasons must be written out completely with “if-then” statements.

You may use abbreviations and symbols you see me use in notes - rt., comp., supp.,
midpt.,  ,  , s ,  , s ,  , ≅. Do not make up your own shorthand!

Statements used to prove s  must be identified (label either “A” or “S” in the left
margin beside the number of the statement) see example below

Concluding reason must include numbers of statements that allow you to reach the
conclusion. (for example: 1,2,4)
see example below
Example:
Given:
Prove:
SV bisects  TSB
VS bisects  TVB
T
S
 TSV   BSV
B
STATEMENTS
1.
A 2.
SV bisects  TSB
 TSV   BSV
3.
A 4.
VS bisects  TVB
 TVS   BVS
S
SV  SV
6.  TSV   BSV
5.
V
REASONS
1. Given
2. If a ray bisects an
3. Given
 , it  it into 2  s .
4. same as 2
5. Reflexive Property
6. ASA Postulate (2,5,4)
Memorize
To successfully complete geometry proofs, you must memorize each definition, property,
postulate, theorem and corollary. Memorize. Do not just become familiar with them; memorize
them. They are the steps one uses to solve geometry problems, called proofs.
Memorize the content not just the number. This seems like more work but it will actually help
you solve the problems. In the proof you may find words that will clue you to the next step. A
number would not give you the hint you needed.
And secondly, not all geometry courses use the exact same numbering system; therefore you
must learn the concepts.
Two geometry students were asked what advice they would give a student just starting geometry.
Both immediately said, “Memorize!”
Hints
1. Work forward as far as you can. Then work backward. See if you can fill in the middle.
2. Mark your drawing as you go. Have a reason for every mark you make and be sure you write
it in your proof.
3. Use every bit of given information. Make certain you don’t overlook a given fact.
4. Read the most recently taught concepts again. Often proofs are placed in the text in certain
places because of the skills they require.
Notes
Even though I am sure you will memorize everything, you should keep notes of each item
because there is much to memorize. Seeing the notes may remind you of forgotten concepts.
Some students keep a notebook, or handbook, of information in the order taught. Others organize
it by concept or type (lines, triangles, definitions, postulates…). Some students use note cards so
they can be reorganized as best fits the current lessons. Other students keep the notes on the
computer and print it out when needed. Some students use color to organize the information.
Tests
Know what is expected and be prepared. Geometry proofs on tests will be similar to those
assigned and in the examples. Know the common pattern of proofs that you have studied. The
test is meant to check your ability to use what you have practiced. The proofs will be like those
you have studied.
Adapted from material by Marilyn Brown, Mark Ryan and Frankie Shillington
Section 1.2 Supplemental Theorems
If a segment is added to two congruent segments, then the sums are congruent.
If an angle is added to two congruent angles, then the sums are congruent.
If congruent segments are added to congruent segments, then the sums are congruent.
If congruent angles are added to congruent angles, then the sums are congruent.
If a segment (or angle) is subtracted from congruent segments (or angles), then the
differences are congruent.
If congruent segments (or angles) are subtracted from congruent segments (or angles), then
the differences are congruent.
Section 1.3 Supplemental Theorems
If segments (or angles) are congruent, then their like multiples are congruent.
If segments (or angles) are congruent, then their like divisions are congruent.
Sample Proof for WS 1.3C
Given: A  60
B  60
Prove: A  B
Statements
Reasons
1. A  60
1. Given
2. B  60
2. Given
3. A  B
3. If two angles have the same measure, then they
are congruent.
Section 1.4 Supplemental Theorems
If two angles are straight angles, then they are congruent.
Sample Proof for WS 1.4B
Section 1.5 Supplemental Theorems
If two angles are right angles, then they are congruent.
If two angles are both supplementary and congruent, then they are right angles.
Sample Proof for WS 1.5B