Proofs, Postulates, Theorems

Complete the conclusion by filling in missing information.

Use one of the theorems, postulates, or definitions to fill in the REASON.

a

b

Substitution Postulate

Angle Addition Postulate

Supplementary

Definition of Angle Bisector

Transitive Property

Complementary

Definition of Supplementary

Complete the conclusion by filling in missing information.

Use one of the theorems, postulates, or definitions to fill in the REASON.

a

d

Definition of Supplementary

Right Angles Theorem

Definition of Angle Bisector

Angle Addition Postulate

+

Definition of Congruent

Definition of Linear Pair

Complete the conclusion by filling in missing information. Use one of the theorems, postulates, or definitions to fill in the REASON.

a

b

j

Definition of Congruent

Definition of Angle Bisector

Linear Pair

Right Angles Theorem

Angle Addition Postulate

Complementary Pair

Definition of Linear Pair

Right Angle

Complete the conclusion by filling in missing information.

Use one of the theorems, postulates, or definitions to fill in the REASON.

a

b

Linear Pair Postulate

Supplementary

Vertical Angles Theorem

Right Angle Theorem

Definition of Congruent

Complementary

Definition of Angle Bisector

Complete the conclusion by filling in missing information.

Use one of the theorems, postulates, or definitions to fill in the REASON.

a

b

Angle Addition Postulate

Definition of Angle Bisector

Definition of Complementary

Transitive Property

Angle Bisector

Definition of Congruent

Complete the conclusion by filling in missing information.

Use one of the theorems, postulates, or definitions to fill in the REASON.

a

b

Symmetric Properety

Vertical Angle Theorem

Angle Addition Postulate

Definition of Complementary

Supplementary

Complementary

Substitution Postulate

Transitive Property

Complete the conclusion by filling in missing information. Use one of the theorems, postulates, or definitions for the REASON.

a

b

c

Definition of Linear Pair

Vertical Angles Theorem

Angle Addition Postulate

Substitution Postulate

Definition of Congruent

Definition of Angle Bisector

Name the property of equality or congruence that justifies going from the first statement to the second statement.

• Reflexive Property of Equality

• Symmetric Property of Equality

• Symmetric Property of Congruence

• Reflexive Property of Congruence

Name the property of equality or congruence that justifies going from the first statement to the second statement.

• Reflexive Property of Congruence

• Symmetric Property of Congruence

• Distributive Property

• Transitive Property of Congruence

Given: ∠1 and ∠3 are vertical angles. What should you conclude by the vertical angles theorem?

• undefined andundefined are right angles.