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.
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.
1 answer
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