Download Introduction to Geometry Proofs

Introduction to
Geometry Proofs
Proof Vocabulary
Axiom
 Postulate
 Theorem



Click here to look up these words on Merriam
Webster’s website. Write them in your Geometry
notebook in your own words.
Look in the appendices in your textbook and find an
example of each.
Logical Argument in Algebra
Click here to watch an example.
Given x + y = 60
 Given x = 5
 Prove y = 55


Use your algebra knowledge to write
a proof. Justify each step you write.
Algebra Proof Solution

Follow the steps.

Justify the steps.



x + y = 60
x=5
5 + y = 60

y = 55

Given
Given
Substitution
Property of Equality
Subtraction Property
of Equality



Types of Geometry Proof
Vocabulary cards are at
Classzone.com

Paragraph Proofs


Flow Chart Proofs


Find an example in your textbook and read it to
your table partner.
Find an example in your textbook and copy the
steps into your Geometry notebook.
Two Column Proofs

This third example is the most commonly used type
of proof. We will focus on this type of proof in class.
Paragraph Proof


Given BA ┴ BC
Prove angle 3 and 4 are complementary
A
D
3
4
B
C
Because BA ┴ BC, angle ABC is a ________ and the measure = _______.
According to the ________ Postulate, the measure of angle 3 + the
measure of angle 4 = the measure of angle ABC. So, by the substitution
property of equality, ________ + ________ = ________. By definition,
angle 3 and angle 4 are complementary.
Flow Chart Proofs
j
5 6
k
Given: angle 5 is congruent to angle 6, angle 5 and 6 are a linear pair.
Prove: j is perpendicular to k.
Put the following statements in the proper order to complete the proof.
When you have finished, compare your solution to your partners.
j is perpendicular to k
2(measure of 5) = 180°
angle 5 is congruent to angle
6
measure of 5 + measure of 5 = 180°
measure of 5 = 90°
measure of 5 + measure of 6 = 180°
angle 5 and angle 6 are supplementary
measure of 5 = measure of 6
angles 5 and 6 are a linear pair.
angle 5 is a right angle
Flow Chart Proofs
j
5 6
k
Given: angle 5 is congruent to angle 6, angle 5 and 6 are a linear
pair.
Prove: j is perpendicular to k.


Now that you have the statements in a logical order, add a
reason to each statement. Reasons are based on properties,
postulates and theorems.
When you have finished, bring your paper to the teacher. You
will be asked to explain your reasoning.
Two Column Proofs
Ask Dr. Math is a great place to start.


Statements
In this column we write
the logical steps that
lead us to the end result.


Reasons
For each statement, we
must use a postulate or
theorem that supports
the statement.
Two Column Proof
Fill in the blanks to complete the proof of the
Reflexive Property of the Congruence of Angles.




Statements
A is an angle.
Measure of A = Measure of A
Angle A is congruent to
Angle A




Reasons
______________________
______________________
______________________
Two Column Proof
Check your solution for the proof of the
Reflexive Property of the Congruence of Angles.




Statements
A is an angle.
Measure of A = Measure of A
Angle A is congruent to
Angle A




Reasons
Given
Reflexive Property of Equality
Definition of Congruent Angles
One last 2 Column Proof
n
2
m
3 1
Complete the following proof by filling in the blanks.
Given: Angle 1 and Angle 2 are supplementary
Prove: n is parallel to m
Statements
1) Angle 1 and Angle 2 are supplementary.
2) Angle 1 and Angle 3 are a linear pair.
3)_____________________________
4)_____________________________
5) n is parallel to m.
Reasons
1)______________________
2)______________________
3) Linear Pair Postulate
4) Congruent Supplements Theorem
5) ______________________
One last 2 Column Proof
n
2
m
3 1
Check your work to see how well you are doing.
Given: Angle 1 and Angle 2 are supplementary
Prove: n is parallel to m
Statements
1) Angle 1 and Angle 2 are supplementary.
2) Angle 1 and Angle 3 are a linear pair.
3) Angle 1 and Angle 3 are supplementary.
4) Angle 2 is congruent to Angle 3
5) n is parallel to m.
Reasons
1) Given
2) Definition of Linear Pair
3) Linear Pair Postulate
4) Congruent Supplements Theorem
5) Corresponding Angles Converse