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Answer:
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Corresponding angles theorem
Step-by-step explanation:
Type of lines of lines a and b = Horizontal and parallel lines
The transversal to a and b = Line c
The angles between a and c labelled clockwise from the upper left quarter segment = 1, 2, 4 and 3
The angles between b and c labelled clockwise from the upper left segment = 5, 6, 8 and 7
Therefore, we have;
Statement Reason
1. a║b, c is a transversal Given
2. ∠6 ≅ ∠2 Corresponding angles theorem
3. m∠6 = m∠2 Definition of congruent
4. ∠6 is supp. to ∠8 Definition of linear pair
5. ∠2 is supp. to ∠8 Congruent supplement theorem
Corresponding angles are the angles located in spatially similar or matching corners of two lines that have been crossed by the same transversal. When the two lines having a common transversal are parallel, the corresponding angles will be congruent.