Corresponding Angles Flow Proof
Given: m angle 5 equals 40 degrees, m angle 2 equals 140 degrees
Prove: line a is parallel to line b
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. A flow chart is shown.
Since the flow chart is not provided, I cannot label the steps directly. However, I can provide you with the general flow of a corresponding angles flow proof and the reasons for each statement:
Flow of the Corresponding Angles Flow Proof:
1. Given: m∠5 = 40°, m∠2 = 140°.
2. ∠2 and ∠5 are corresponding angles with respect to lines a and b.
3. Corresponding angles of a transversal intersecting two parallel lines are congruent.
4. Therefore, m∠2 = m∠5.
5. Since m∠2 = 140° and m∠5 = 40°, angles 2 and 5 are congruent.
6. From statement 5, we can conclude that line a is parallel to line b.
Reasons for Each Statement:
a. Given: This statement specifies the initial information provided in the problem.
b. Definition of corresponding angles: Corresponding angles are formed when a transversal intersects two parallel lines and are located in corresponding positions with respect to the transversal and the parallel lines.
c. Corresponding angles postulate: This postulate states that when a transversal intersects two parallel lines, the corresponding angles formed are congruent.
d. Substitution property of equality: This property allows us to substitute equal quantities for each other in an equation.
e. Conclusion based on congruent angles: If two angles are congruent, then the lines they are corresponding to must be parallel.
Note: The specific labeling of the steps may vary depending on the flow chart provided in the question.
Unfortunately, I cannot see the flow chart you mentioned as I am a text-based AI. However, I can help you understand the steps you need to follow in order to prove that line a is parallel to line b using the given information:
Given: m∠5 = 40 degrees, m∠2 = 140 degrees
To prove: a ∥ b
Step a: Given
Reason for step a: It is given that m∠5 = 40 degrees.
Step b: Corresponding angles are congruent.
Reason for step b: Corresponding angles on parallel lines are congruent.
Step c: m∠5 = m∠2
Reason for step c: It is given that m∠5 = 40 degrees and m∠2 = 140 degrees.
Step d: m∠2 = 40 degrees.
Reason for step d: By the transitive property of equality, since m∠5 = m∠2 and m∠5 = 40 degrees, it follows that m∠2 = 40 degrees.
Step e: Line a is parallel to line b.
Reason for step e: By the definition of parallel lines, if the corresponding angles are congruent, then the lines are parallel.
Therefore, the flow proof should include the steps: a, b, c, d, and e with their respective reasons as mentioned above.
Since I don't have access to the actual flow chart you're referring to, I can explain the reasons for each statement in a verbal form based on the given information.
Given:
m∠5 = 40 degrees
m∠2 = 140 degrees
To prove: line a is parallel to line b
Flow Proof:
Step a:
Statement: ∠5 and ∠2 are corresponding angles.
Reason: When two lines are intersected by a transversal, the angles in the same position on the same side of the transversal are called corresponding angles.
Step b:
Statement: Corresponding angles are congruent.
Reason: Corresponding angles formed by a transversal and two parallel lines are congruent.
Step c:
Statement: m∠5 = m∠2
Reason: Since ∠5 and ∠2 are corresponding angles, they are congruent.
Step d:
Statement: m∠5 = 40 degrees and m∠2 = 140 degrees
Reason: Given from the initial information.
Step e:
Statement: If two angles of a pair of corresponding angles are congruent, then the lines containing the angles are parallel.
Reason: This is a property of corresponding angles. If corresponding angles are congruent, then the lines containing those angles are parallel.
Therefore, based on the flow proof, statement e concludes that line a is parallel to line b. The main reasoning behind this is the congruence of corresponding angles (statement b), which demonstrates the parallelism of the lines.