Lesson 2.4AIM: Properties of Equality

and Congruence

DO NOW: Draw a conclusion from the following statements.

1. If an integer ends in 4, it is divisible by 2.

2. If an integer is divisible by 2, it is even.

CONCLUSION: If an integer ends in 4, it is even.

The Reflexive Property states

I am as tall as myself.

The Symmetric Property states

If I am as tall as my brother,

my brother is as tall as me.

The Transitive Property states

If I am as tall as my brother, and my brother is as tall as my cousin,

I am as tall as my cousin.

Name the Property

a. Symmetric Property

b. Reflexive Property

c. Transitive Property

Prove MN = PQ

STATEMENT JUSTIFICATION

Prove MN = PQ

STATEMENT

1. MN = NP

JUSTIFICATION

1. Definition of Midpoint

Prove MN = PQ

STATEMENT

1. MN = NP

2. NP = PQ

JUSTIFICATION

1. Definition of Midpoint

2. Definition of Midpoint

Prove MN = PQ

STATEMENT

1. MN = NP

2. NP = PQ

3. MN = PQ

JUSTIFICATION

1. Definition of Midpoint

2. Definition of Midpoint

3. Transitive Property

Prove Angle 1 is Congruent to Angle 2

STATEMENT JUSTIFICATION

Prove Angle 1 is Congruent to Angle 2

STATEMENT

1. A 1 + A 3 = 180

JUSTIFICATION

1. Definition of Supplementary

Prove Angle 1 is Congruent to Angle 2

STATEMENT

1. A 1 + A 3 = 180

2. A 2 + A 3 = 180

JUSTIFICATION

1. Definition of Supplementary

2. Definition of Supplementary

Prove Angle 1 is Congruent to Angle 2

STATEMENT

1. A 1 + A 3 = 180

2. A 2 + A 3 = 180

3. A 1 + A 3 = A 2 + A 3

JUSTIFICATION

1. Definition of Supplementary

2. Definition of Supplementary

3. Substitution Property

Prove Angle 1 is Congruent to Angle 2

STATEMENT

1. A 1 + A 3 = 180

2. A 2 + A 3 = 180

3. A 1 + A 3 = A 2 + A 3

- A 3 - A 3

JUSTIFICATION

1. Definition of Supplementary

2. Definition of Supplementary

3. Substitution Property

STATEMENT

1. A 1 + A 3 = 180

2. A 2 + A 3 = 180

3. A 1 + A 3 = A 2 + A 3

- A 3 - A 3

4. A1 = A2

JUSTIFICATION

1. Definition of Supplementary

2. Definition of Supplementary

3. Substitution Property

4. Subtraction Property of Equality

Prove Angle 1 is Congruent to Angle 2

Summary Question

Identify the following property:

If AB = BC and BC = CD, then AB = CD.