The flow proof shows the statements that lead to the conclusion that a∥b in the diagram. The reasons for each statement in the flow proof are missing. Identify the reasons for each of the 5 statements shown in the flow proof. In your response, label the steps a-e.
1. m<5 = 40 degrees
2. m<2 = 140 degrees
3. <5 and <2 and supplementary angles
4. <5 and <2 and same-side interior angles
5. a//b
a. Given
b. Given
c. Definition of supplementary angles
d. Definition of same-side interior angles
e. Transitive property of parallel lines
Below are the reasons for each of the statements in the flow proof:
a. Given (or supplementary angles)
b. Given (or supplementary angles)
c. Definition of supplementary angles
d. Definition of same-side interior angles
e. Definition of parallel lines (two lines are parallel if they have the same-side interior angles)
To determine the reasons for each of the statements in the flow proof, let's analyze the given information step by step:
a) Statement: m<5 = 40 degrees
Reason: This statement could be supported by a given angle measurement, a diagram showing the given angle measurement, or prior information within the problem context.
b) Statement: m<2 = 140 degrees
Reason: Similar to statement a), this statement could be supported by a given angle measurement, a diagram showing the given angle measurement, or prior information within the problem context.
c) Statement: <5 and <2 are supplementary angles
Reason: The reason behind this statement is that if angles <5 and <2 are both given, or if m<5 = 40 degrees and m<2 = 140 degrees, then they are supplementary angles by definition.
d) Statement: <5 and <2 are same-side interior angles
Reason: Depending on the context and diagram provided, this statement may not be directly stated or assumed. However, it could be inferred based on the transversal cutting through the two lines a and b, which form the angles <5 and <2.
e) Statement: a ∥ b (a is parallel to b)
Reason: Since statements c) and d) state that <5 and <2 are supplementary and same-side interior angles, it can be concluded that the lines a and b are parallel (denoted by a ∥ b).
Overall, the reasons for each statement in the flow proof are as follows:
a) Given or Prior Information
b) Given or Prior Information
c) Definition of Supplementary Angles
d) Inference based on the diagram and information provided
e) Conclusion based on statements c) and d)