Question

same - side interior angle theorem
given (lparallel m). prove (angle2) and (angle5) are supplementary.
statements: 1. (lparallel m); 2. (angle1=angle5); 3. (mangle1 = mangle5); 4. (angle1) and (angle2) are a linear pair; 5. (angle1) and (angle2) are supplementary; 6. (mangle1 + mangle2=180^{circ}); 7. (mangle5 + mangle2 = 180^{circ}); 8. (angle5) and (angle2) are supplementary.
reasons: 1. given; 2. to be filled; 3. definition of congruent angles; 4. definition of a linear pair; 5. linear pair postulate; 6. definition of supplementary angles; 7. to be filled; 8. definition of supplementary angles.

1. which theorem completes reason 2? (a) a. alternate interior angle theorem b. corresponding angle theorem c. same - side interior angle theorem d. same - side exterior angle theorem e. alternate exterior angle theorem (b) what completes reason 7? a. definition of supplementary angle b. substitution property

Explanation:

(a) Since we are given two parallel lines \(l\) and \(m\) and we are going from the statement \(\angle1=\angle5\) (congruent angles), the theorem that justifies this when dealing with parallel - lines and angles in this position is the Corresponding Angle Theorem.
(b) We know that \(m\angle1 + m\angle2=180^{\circ}\) (from linear - pair postulate) and \(m\angle1 = m\angle5\). To get from \(m\angle1 + m\angle2=180^{\circ}\) to \(m\angle5 + m\angle2=180^{\circ}\), we use the Substitution Property.

Answer:

(a) B. Corresponding Angle Theorem
(b) B. Substitution Property