Questions and Answers
What is the definition of congruence?
What does an angle bisector do?
An angle bisector divides an angle into two equal parts.
What is the definition of complementary angles?
Complementary angles sum to 90°.
What is the definition of supplementary angles?
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Perpendicular lines form right angles.
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What is a right angle?
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What does the Angle Addition Postulate state?
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If two angles are vertical, they are congruent.
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What does the Complement Theorem state?
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What does the Supplement Theorem state?
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What does the Congruent Complements Theorem state?
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What does the Congruent Supplements Theorem state?
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Study Notes
Definitions of Angle Relationships
- Congruence: Symbolically represented as m∠A = m∠B ↔ ∠A ≅ ∠B, indicates that two angles have the same measure.
- Angle Bisector: A line or ray that divides an angle into two equal smaller angles, ensuring both parts have equal measurement.
Types of Angle Pairs
- Complementary Angles: Two angles that add up to 90°, always forming a right angle when combined.
- Supplementary Angles: Two angles whose measures total 180°, resulting in a straight line when placed adjacent.
Properties of Angles
- Perpendicular Lines: These lines intersect to form right angles (90°); a fundamental concept in geometry that establishes a square relationship.
- Right Angle: Defined specifically as an angle that measures 90°, serving as a benchmark for measuring other angles.
Angle Relationships and Theorems
- Angle Addition Postulate: For angles AOB and BOC, the measure of angle AOC can be found by adding the measures of angles AOB and BOC, represented as m∠AOB + m∠BOC = m∠AOC.
- Vertical Angles Theorem: States that when two angles are formed by two intersecting lines, the angles opposite each other (vertical angles) are congruent.
Theorems Involving Complementary and Supplementary Angles
- Complement Theorem: If two angles form a right angle (90°), those two angles are complementary.
- Supplement Theorem: This theorem states that if two angles form a linear pair (they are adjacent and supplementary), they add up to 180°.
- Congruent Compliments Theorem: If angle A is complementary to angle B, and angle C is also complementary to angle B, then angle A is congruent to angle C (∠A ≅ ∠C).
- Congruent Supplements Theorem: Similar to the complementary theorem, if angle A is supplementary to angle B, and angle C is also supplementary to angle B, then angle A is congruent to angle C (∠A ≅ ∠C).
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Test your knowledge of key angle proofs and definitions with these flashcards. Each card covers essential concepts such as congruence, angle bisectors, and complementary angles. Perfect for students studying geometry and preparing for exams.
