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Mathematics, 06.11.2020 22:50 DEVlN6070

Line AB is parallel to EF. Transversal GJ crosses line AB at K and crosses line EF at L. The measure of angle ELJ is 120 degrees. Daniel is constructing a fence that consists of parallel sides line AB and line EF. Complete the proof to explain how he can show that māˆ GKB = 120Ā° by filling in the missing justifications.

Statement Justification
line AB āˆ„ line EF
māˆ ELJ = 120Ā° Given
māˆ ELJ + māˆ ELK = 180Ā° Linear Pair Postulate
māˆ BKL + māˆ GKB = 180Ā° Linear Pair Postulate
māˆ ELJ + māˆ ELK = māˆ BKL + māˆ GKB Transitive Property
āˆ ELK ā‰… āˆ BKL 1.
māˆ ELK = māˆ BKL 2.
māˆ ELJ + māˆ ELK = māˆ ELK + māˆ GKB Substitution Property
māˆ ELJ = māˆ GKB Subtraction Property
māˆ GKB = māˆ ELJ Symmetric Property
māˆ GKB = 120Ā° Substitution
A 1. Alternate Interior Angles Theorem; 2. Definition of Congruence
B 1. Alternate Exterior Angles Theorem; 2. Substitution Property
C 1. Definition of Congruence; 2. Alternate Interior Angles Theorem
D 1. Substitution Property; 2. Alternate Exterior Angles Theorem

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Line AB is parallel to EF. Transversal GJ crosses line AB at K and crosses line EF at L. The measure...
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