Match the justifications for each step in order to complete the proof. Note that lines p and r are parallel. (2 points) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. ∠1≅∠5∠1≅∠5 p∥rp∥r ∠4≅∠1∠4≅∠1 ∠4≅∠5∠4≅∠5
1) ∠1≅∠5
2) ∠4≅∠1
3) ∠4≅∠5
4) p∥r
Match the justifications for each step in order to complete the proof. Note that lines p and r are parallel. (2 points) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
∠1≅∠5
p∥q
∠4≅∠1
∠4≅∠5
transitive property
given
alternate exterior angles converse
vertical angles
1) ∠1≅∠5 - vertical angles
2) p∥q - given
3) ∠4≅∠1 - alternate exterior angles converse
4) ∠4≅∠5 - transitive property
Use the diagram to answer the question. Corresponding Angles Flow Proof Given: Prove: Angle 1 is on right side of intersecting line and above top line a. Angle 2 is on left side of intersecting line and under top line. Angle 4 is on right side of intersecting line and above line b. Angle 5 is on left side of intersecting line and above line b c. The flow proof shows the statements that lead to the conclusion that a∥ba∥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. Angle 1 is on right side of intersecting line and above top line
b. Angle 2 is on left side of intersecting line and under top line
c. Angle 4 is on right side of intersecting line and above line b
d. Angle 5 is on left side of intersecting line and above line b
e. Conclusion: a∥b
Reasons for each statement in the flow proof:
a. Definition of an angle on the right side of a line
b. Definition of an angle on the left side of a line
c. Definition of an angle on the right side of a line
d. Definition of an angle on the left side of a line
e. Corresponding angles converse or alternate interior angles converse
To complete the proof, we need to match the justifications for each step. Here is the correct matching:
Step 1: ∠1 ≅ ∠5 (Given)
Step 2: p ∥ r (Given)
Step 3: ∠4 ≅ ∠1 (Alternate Interior Angles Theorem)
Step 4: ∠4 ≅ ∠5 (Transitive Property of Congruence)
To complete the proof, we need to match the justifications for each step given the statements provided. Let's analyze the statements and their relationships:
Statements:
1) ∠1 ≅ ∠5
2) p ∥ r (Lines p and r are parallel)
3) ∠4 ≅ ∠1
4) ∠4 ≅ ∠5
Justifications:
a) Corresponding Angles Postulate
b) Transitive Property
c) Definition of Parallel Lines
d) Substitution Property
Now let's match the justifications with their corresponding steps:
Step 1: ∠1 ≅ ∠5
- Justification: a) Corresponding Angles Postulate
Step 2: p ∥ r (Lines p and r are parallel)
- Justification: c) Definition of Parallel Lines
Step 3: ∠4 ≅ ∠1
- Justification: d) Substitution Property
Step 4: ∠4 ≅ ∠5
- Justification: b) Transitive Property
So the matches are as follows:
Step 1: ∠1 ≅ ∠5, Justification: a) Corresponding Angles Postulate
Step 2: p ∥ r, Justification: c) Definition of Parallel Lines
Step 3: ∠4 ≅ ∠1, Justification: d) Substitution Property
Step 4: ∠4 ≅ ∠5, Justification: b) Transitive Property