Introduction toGeometry Proofs

Proof Vocabulary

Axiom Postulate Theorem

Click here to look up these words on MerriamWebster’s website. Write them in your Geometrynotebook in your own words.

Look in the appendices in your textbook and find anexample of each.

Axiom Postulate Theorem

Click here to look up these words on MerriamWebster’s website. Write them in your Geometrynotebook in your own words.

Look in the appendices in your textbook and find anexample of each.

Logical Argument in AlgebraClick here to watch an example.

Given x + y = 60 Given x = 5 Prove y = 55

Use your algebra knowledge towrite a proof. Justify each step youwrite.

Given x + y = 60 Given x = 5 Prove y = 55

Use your algebra knowledge towrite a proof. Justify each step youwrite.

Algebra Proof Solution

Follow the steps.

x + y = 60 x = 5 5 + y = 60

y = 55

Justify the steps.

Given Given Substitution

Property of Equality Subtraction

Property of Equality

Follow the steps.

x + y = 60 x = 5 5 + y = 60

y = 55

Justify the steps.

Given Given Substitution

Property of Equality Subtraction

Property of Equality

Types of Geometry ProofVocabulary cards are at

Classzone.com Paragraph Proofs

Find an example in your textbook and read it toyour table partner.

Flow Chart Proofs 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 Proofs Find an example in your textbook and read it to

your table partner.

Flow Chart Proofs 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

Fill in the blanks in the following paragraph proof(p.139, #17). Check your answers at hotmath.com.(password is CA31682AC)

Given BA ┴ BC Prove angle 3 and 4 are complementary A D

34

B C

Because BA ┴ BC, angle ABC is a ________ and the measure = _______.According to the ________ Postulate, the measure of angle 3 + themeasure of angle 4 = the measure of angle ABC. So, by the substitutionproperty of equality, ________ + ________ = ________. By definition,angle 3 and angle 4 are complementary.

Fill in the blanks in the following paragraph proof(p.139, #17). Check your answers at hotmath.com.(password is CA31682AC)

Given BA ┴ BC Prove angle 3 and 4 are complementary A D

34

B C

Because BA ┴ BC, angle ABC is a ________ and the measure = _______.According to the ________ Postulate, the measure of angle 3 + themeasure of angle 4 = the measure of angle ABC. So, by the substitutionproperty of equality, ________ + ________ = ________. By definition,angle 3 and angle 4 are complementary.

Flow Chart Proofsj

5 6k

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

5 6k

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.

angle 5 is congruent to angle6

j is perpendicular to k measure of 5 = 90°

measure of 5 = measure of 6angles 5 and 6 are a linear pair.

2(measure of 5) = 180°

measure of 5 + measure of 6 = 180°

angle 5 and angle 6 are supplementary

angle 5 is a right angle

measure of 5 + measure of 5 = 180°

Flow Chart Proofsj

5 6k

Given: angle 5 is congruent to angle 6, angle 5 and 6 are a linearpair.

Prove: j is perpendicular to k.

Now that you have the statements in a logical order, add areason to each statement. Reasons are based on properties,postulates and theorems.

When you have finished, bring your paper to the teacher. Youwill be asked to explain your reasoning.

j

5 6k

Given: angle 5 is congruent to angle 6, angle 5 and 6 are a linearpair.

Prove: j is perpendicular to k.

Now that you have the statements in a logical order, add areason to each statement. Reasons are based on properties,postulates and theorems.

When you have finished, bring your paper to the teacher. Youwill be asked to explain your reasoning.

Two Column ProofsAsk Dr. Math is a great place to start.

Statements

In this column we writethe logical steps thatlead us to the end result.

Reasons

For each statement, wemust use a postulate ortheorem that supportsthe statement.

Statements

In this column we writethe logical steps thatlead us to the end result.

Reasons

For each statement, wemust use a postulate ortheorem that supportsthe statement.

Two Column ProofFill 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

______________________ ______________________ ______________________

Statements

A is an angle. Measure of A = Measure of A Angle A is congruent to

Angle A

Reasons

______________________ ______________________ ______________________

Two Column ProofCheck 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

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 Proofn m

2 3 1

Complete the following proof by filling in the blanks.

Given: Angle 1 and Angle 2 are supplementaryProve: n is parallel to m

Statements Reasons1) Angle 1 and Angle 2 are supplementary. 1)______________________2) Angle 1 and Angle 3 are a linear pair. 2)______________________3)_____________________________ 3) Linear Pair Postulate4)_____________________________ 4) Congruent Supplements Theorem5) n is parallel tom. 5) ______________________

n m2 3 1

Complete the following proof by filling in the blanks.

Given: Angle 1 and Angle 2 are supplementaryProve: n is parallel to m

Statements Reasons1) Angle 1 and Angle 2 are supplementary. 1)______________________2) Angle 1 and Angle 3 are a linear pair. 2)______________________3)_____________________________ 3) Linear Pair Postulate4)_____________________________ 4) Congruent Supplements Theorem5) n is parallel tom. 5) ______________________

One last 2 Column Proofn m

2 3 1

Check your work to see how well you are doing.

Given: Angle 1 and Angle 2 are supplementaryProve: n is parallel to m

Statements Reasons1) Angle 1 and Angle 2 are supplementary. 1) Given2) Angle 1 and Angle 3 are a linear pair. 2) Definition of Linear Pair3) Angle 1 and Angle 3 are supplementary. 3) Linear Pair Postulate4) Angle 2 is congruent to Angle 3 4) Congruent Supplements Theorem5) n is parallel tom. 5) Corresponding Angles Converse

n m2 3 1

Check your work to see how well you are doing.

Given: Angle 1 and Angle 2 are supplementaryProve: n is parallel to m

Statements Reasons1) Angle 1 and Angle 2 are supplementary. 1) Given2) Angle 1 and Angle 3 are a linear pair. 2) Definition of Linear Pair3) Angle 1 and Angle 3 are supplementary. 3) Linear Pair Postulate4) Angle 2 is congruent to Angle 3 4) Congruent Supplements Theorem5) n is parallel tom. 5) Corresponding Angles Converse