Questions and Answers
What does the Addition Property of Equality state?
What does the Subtraction Property of Equality state?
What does the Multiplication Property of Equality state?
What does the Division Property of Equality state?
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What is the Reflexive Property of Equality?
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What does the Symmetric Property of Equality state?
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What does the Transitive Property of Equality indicate?
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What is the Substitution Property of Equality?
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The Distributive Property states that A(B+C) = ________.
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Define congruent angles.
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All right angles are congruent.
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What does the Congruent Supplements Theorem state?
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What does the Congruent Complements Theorem state?
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If two angles form a linear pair, then they are supplementary.
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Vertical angles are congruent.
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What is the Parallel Postulate?
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What does the Perpendicular Postulate indicate?
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What is the first Perpendicular Line Theorem?
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What does the second Perpendicular Line Theorem state?
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What does the third Perpendicular Line Theorem state?
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What is the Corresponding Angles Postulate?
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What does the Alternate Interior Angles Theorem state?
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What does the Consecutive Interior Angles Theorem indicate?
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What does the Alternate Exterior Angles Theorem state?
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What does the Perpendicular Transversal Theorem indicate?
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What does the Corresponding Angles Converse state?
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What does the Alternate Interior Angles Converse state?
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What does the Consecutive Interior Angles Converse indicate?
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What does the Alternate Exterior Angles Converse state?
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Study Notes
Properties of Equality
- Addition Property of Equality: If A=B, then A+C=B+C, allowing addition to both sides of an equation.
- Subtraction Property of Equality: If A=B, then A-C=B-C, permitting subtraction on both sides of an equation.
- Multiplication Property of Equality: If A=B, then AC=BC, enabling multiplication of both sides by the same factor.
- Division Property of Equality: If A=B and C≠0, then A/C = B/C, allowing division of both sides by a non-zero value.
Properties of Equality Continued
- Reflexive Property of Equality: For any real number A, A=A demonstrates a number is equal to itself.
- Symmetric Property of Equality: If A=B, then B=A shows the relationship is reversible.
- Transitive Property of Equality: If A=B and B=C, then A=C allows for the transitive relationship of equality.
- Substitution Property of Equality: If A=B, then A can be substituted for B in expressions.
Fundamental Properties
- Distributive Property of Equality: A(B+C)=AB+AC illustrates distributing multiplication over addition.
Angle Definitions and Theorems
- Definition of Congruent Angles: Two angles are congruent if they have the same measure.
- Right Angle Congruence Theorem: All right angles are congruent, establishing equality among all right angles.
Supplementary and Complementary Angles
- Congruent Supplements Theorem: Angles supplementary to the same angle or to congruent angles are congruent.
- Congruent Complements Theorem: Angles complementary to the same angle are congruent.
- Linear Pair Postulate: A linear pair of angles are supplementary, leading to a total of 180 degrees.
Vertical Angles
- Vertical Angles Theorem: Vertical angles are always congruent, forming equal angles when two lines intersect.
Postulates about Lines
- Parallel Postulate: Through a point not on a given line, exactly one parallel line can be drawn.
- Perpendicular Postulate: Through a point not on a given line, exactly one perpendicular line can be drawn.
Theorems about Perpendicular Lines
- Perpendicular Line Theorem #1: If two lines intersect to form congruent angles, the lines are perpendicular.
- Perpendicular Line Theorem #2: If angles are adjacent and their sides are perpendicular, the angles are complementary.
- Perpendicular Line Theorem #3: Perpendicular lines intersect to form right angles.
Angle Relationships with Transversals
- Corresponding Angles Postulate: If parallel lines are cut by a transversal, corresponding angles are congruent.
- Alternate Interior Angles Theorem: Alternate interior angles formed by parallel lines and a transversal are congruent.
- Consecutive Interior Angles Theorem: Consecutive interior angles are supplementary when parallel lines are cut by a transversal.
- Alternate Exterior Angles Theorem: Alternate exterior angles are congruent when parallel lines are intersected by a transversal.
Converse Properties
- Perpendicular Transversal Theorem: A transversal perpendicular to one parallel line is also perpendicular to the other.
- Corresponding Angles Converse: If corresponding angles are congruent when two lines are intersected by a transversal, the lines are parallel.
- Alternate Interior Angles Converse: Congruent alternate interior angles imply the lines are parallel.
- Consecutive Interior Angles Converse: Supplementary consecutive interior angles indicate the lines are parallel.
- Alternate Exterior Angles Converse: Congruent alternate exterior angles suggest that the lines are parallel.
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Test your understanding of geometry with flashcards covering essential postulates, theorems, definitions, and properties. This quiz includes fundamental equality properties that are crucial for solving geometric proofs. Prepare to enhance your knowledge and skills in geometry!