Match the justifications for each step in order to complete the proof. Note that lines p and r are parallel.
<4=~ <1
-1=~<5
p || r
<4=~<5
Match:
Alternate Interior Angles converse
vertical angles
Given
Transitive property
1. Alternate Interior Angles converse: <4 =~ <5
2. Transitive property: <4 =~ <1, <1 =~ <5
3. Vertical angles: -1 =~ <5
4. Given: p || r
Step 1: Given
Step 2: p || r (Given)
Step 3: <4 = ~<5 (Alternate Interior Angles converse)
Step 4: -1 = ~<5 (Given)
Step 5: <4 = ~<1 (Vertical Angles)
Step 6: <4 = ~<1 (Transitive Property)
To complete the proof, we need to match each step with its justification. Let's go through the statements and find the corresponding justifications:
Statement:
<4 = ~<1 (Angle 4 is congruent to Angle 1)
-1 = ~<5 (Angle -1 is congruent to Angle 5)
p || r (Lines p and r are parallel)
<4 = ~<5 (Angle 4 is congruent to Angle 5)
Justification:
Alternate Interior Angles converse
Vertical angles
Given
Transitive property
Matching the statements and justifications, we can identify the correct matches:
- Statement: <4 = ~<1 (Angle 4 is congruent to Angle 1)
Justification: Vertical angles
- Statement: -1 = ~<5 (Angle -1 is congruent to Angle 5)
Justification: Alternate Interior Angles converse
- Statement: p || r (Lines p and r are parallel)
Justification: Given
- Statement: <4 = ~<5 (Angle 4 is congruent to Angle 5)
Justification: Transitive property
So, the correct matches are as follows:
- Alternate Interior Angles converse: <4 = ~<1
- Vertical angles: -1 = ~<5
- Given: p || r
- Transitive property: <4 = ~<5