Geometry Angle Proofs Flashcards

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).