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Learn about adjacent angles, linear pairs, vertical angles, and angle congruence theorems in geometry. Practice identifying angles and solving for angle measures in diagrams.
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Lesson 4.6 Angle Pair Relationships Page 223
Adjacent Angles 1. Two angles that share a common vertex and side, but have no common interior points are adjacent angles. C D A B
Linear Pair Two adjacent angles are a linear pair if their noncommon sides are opposite rays. C A D B
Theorem 4.3 Right Angles Congruence Theorem: All right angles are congruent. C A B
Theorem 4.4 Congruent Supplements Theorem: If two angles are supplementary to the same angle (or to congruent angles), then they are congruent.
Theorem 4.5 Congruent Complements Theorem: If two angles are supplementary to the same angle (or to congruent angles), then they are congruent.
Linear Pair Postulate: If two angles form a linear pair, then they are supplementary. 2 1
Theorem 4.6 Vertical Angles Congruence Theorem: Vertical angles are congruent. 1 3 2
Example 2 Find the other angles as well.
#5 Make a sketch of the given information. Label all angles which can be determined.
#6 Make a sketch of the given information. Label all angles which can be determined.
#7 Make a sketch of the given information. Label all angles which can be determined.
#8 Make a sketch of the given information. Label all angles which can be determined.
#9 Make a sketch of the given information. Label all angles which can be determined.
#10 Make a sketch of the given information. Label all angles which can be determined.
#11 Find the value of the variables and the measure of each angle in the diagram.
#12 Find the value of the variables and the measure of each angle in the diagram.
#13 Find the value of the variables and the measure of each angle in the diagram.
#14 Find the value of the variables and the measure of each angle in the diagram.