S7.1 Proofs

Proofs Related to the following theorems: - Complements of the same angle are congruent - Supplements of the same angle are congruent - Complements of congruent angles are congruent - Supplements of congruent angles are congruent - Vertical angles are congruent

Reason 2

Reason 2

Definition of congruent angles

Reason 5

Definition of complementary angles

Reason 6

Definition of complementary angles

Reason 7

Substitution

Reason 8

Subtraction property of equality

Reason 9

Definition of congruent angles

Reason 2

Complements of the same angle are congruent

Reason 3

Definition of congruent angles

Reason 5

Definition of supplementary angles

Reason 6

Substitution

Reason 7

Definition of supplementary angles

Reason 3

Definition of vertical angles

Reason 4

Given

Reason 5

Angles in a linear pair are supplementary

Reason 6

Given

Reason 7

Angles in a linear pair are supplementary

Reason 8

Supplements of the same angle are congruent

Reason 2

Definition of angle bisector

Reason 3

Definition of congruent angles

Reason 4

Definition of vertical angles

Reason 5

Definition of congruent angles

Reason 6

Transitive property

Reason 7

Definition of congruent angles

Reason 2

Given

Reason 3

Definition of supplementary angles

Reason 4

Supplements of the same angle are congruent

Reason 5

Definition of isosceles triangle

Reason 2

Definition of complementary angles

Reason 3

Subtraction property of equality

Reason 4

Property of the angle

Reason 5

Property of equality

Reason 6

Subtraction property of equality

Reason 7

Definition of the acute angle

Reason 3

Angles in a linear pair are supplementary

Reason 4

Supplements of the same angle are congruent

Reason 5

Definition of an isosceles triangle

Reason 1

Given

Reason 2

Linear pair

Reason 3

Supplements of the same angle are congruent

Reason 4

Substitution

Reason 5

Addition property of equality

Reason 6

Division property of equality

Reason 1

Given

Reason 2

Right angles are congruent

Reason 3

Given

Reason 4

Angles in a linear pair are supplementary

Reason 5

Given

Reason 6

Supplements of congruent angles are congruent

Reason 7

Given

Reason 8

ASA

Reason 9

CPCTC

Reason 1

Given

Reason 2

Given

Reason 3

Definition of vertical angles

Reason 4

Vertically opposite angles are congruent

Reason 5

SAS postulate

Reason 6

Corresponding parts of congruent triangles are congruent

Reason 1

Given

Reason 2

Definition of a linear pair

Reason 3

Angles in a linear pair are supplementary

Reason 4

Supplements of same angle are congruent