Podcast
Questions and Answers
What is the definition of congruence?
What is the definition of congruence?
- m∠A = m∠B ↔ ∠A ≅ ∠B (correct)
- an angle bisector divides an angle into two equal parts
- perpendicular lines form right angles
- complementary ↔ sum is 90°
What does an angle bisector do?
What does an angle bisector do?
An angle bisector divides an angle into two equal parts.
What is the definition of complementary angles?
What is the definition of complementary angles?
Complementary angles sum to 90°.
What is the definition of supplementary angles?
What is the definition of supplementary angles?
Perpendicular lines form right angles.
Perpendicular lines form right angles.
What is a right angle?
What is a right angle?
What does the Angle Addition Postulate state?
What does the Angle Addition Postulate state?
If two angles are vertical, they are congruent.
If two angles are vertical, they are congruent.
What does the Complement Theorem state?
What does the Complement Theorem state?
What does the Supplement Theorem state?
What does the Supplement Theorem state?
What does the Congruent Complements Theorem state?
What does the Congruent Complements Theorem state?
What does the Congruent Supplements Theorem state?
What does the Congruent Supplements Theorem state?
Flashcards
Congruent Angles
Congruent Angles
Angles with the same measure are congruent. This means they are equal in size.
What is an angle bisector?
What is an angle bisector?
An angle bisector divides an angle into two equal angles.
Complementary angles
Complementary angles
Two angles are complementary if their measures sum to 90 degrees.
Supplementary angles
Supplementary angles
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Perpendicular Lines
Perpendicular Lines
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What is a right angle?
What is a right angle?
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Angle Addition Postulate
Angle Addition Postulate
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Vertical angles
Vertical angles
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Complement Theorem
Complement Theorem
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Supplement Theorem
Supplement Theorem
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Congruent Complements Theorem
Congruent Complements Theorem
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Congruent Supplements Theorem
Congruent Supplements Theorem
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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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Description
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.
