Lesson 2.4 AIM: Properties of Equality and Congruence

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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.

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The Reflexive Property states

• I am as tall as myself.

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The Symmetric Property states

• If I am as tall as my brother,
• my brother is as tall as me.

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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.

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Name the Property

1. Symmetric Property
2. Reflexive Property
3. Transitive Property

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Prove MN PQ
STATEMENT JUSTIFICATION
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Prove MN PQ
STATEMENT 1. MN NP JUSTIFICATION 1. Definition of Midpoint
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Prove MN PQ
STATEMENT MN NP 2. NP PQ JUSTIFICATION 1. Definition of Midpoint 2. Definition of Midpoint
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Prove MN PQ
STATEMENT MN NP 2. NP PQ 3. MN PQ JUSTIFICATION 1. Definition of Midpoint Definition of Midpoint Transitive Property
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Prove Angle 1 is Congruent to Angle 2
STATEMENT JUSTIFICATION
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Prove Angle 1 is Congruent to Angle 2
STATEMENT A 1 A 3 180 JUSTIFICATION 1. Definition of Supplementary
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Prove Angle 1 is Congruent to Angle 2
STATEMENT A 1 A 3 180 2. A 2 A 3 180 JUSTIFICATION 1. Definition of Supplementary 2. Definition of Supplementary
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Prove Angle 1 is Congruent to Angle 2
STATEMENT 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 Substitution Property
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Prove Angle 1 is Congruent to Angle 2
STATEMENT A 1 A 3 180 2. A 2 A 3 180 A 1 A 3 A 2 A 3 - A 3 - A 3 JUSTIFICATION 1. Definition of Supplementary 2. Definition of Supplementary Substitution Property
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Prove Angle 1 is Congruent to Angle 2
STATEMENT A 1 A 3 180 2. A 2 A 3 180 A 1 A 3 A 2 A 3 - A 3 - A 3 4. A1 A2 JUSTIFICATION 1. Definition of Supplementary 2. Definition of Supplementary Substitution Property 4. Subtraction Property of Equality
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Summary Question

• Identify the following property
• If AB BC and BC CD, then AB CD.