Vertical Angle Theorem
What are vertical angles?
Intersecting Lines
How many vertical angles pairs to these lines form?
Which of the angles are vertical angles? Call the intersection of the two lines O.
What happens to the angles as you change the slope of line (a)? Which angles get narrower and which get wider? Do any changes happen at the same time?
What do you notice about the green angles as you edit the slope of both lines on the sliders? What do you notice about the pink angles as you edit the slopes?
Geometric construction for vertical angle theorem proof
Proof Construction Instructions
| Statements | Reasons |
1. AB intersects CD. | 1. Given |
| 2. | 2. Angle addition postulate |
| 3. ? | 3. Angle addition postulate |
| 4. | 4. Substitution |
| 5. | 5. Subtract ? from both sides |
| 6. | 6. Definition of ? |
Write the correct answer for each of the question marks from the proof above. Use this format: Step 3: answer Step 4: answer Step 5: answer Step 6: answer
Collaborate with a partner
Find a partner who is has finished the question above. Do their line segments from the "Geometric construction for vertical angle theorem proof" look the same as yours? If not discuss with your partner why their proof work the same way yours does despite this difference. If their line segments are exactly the same, move yours and then discuss with your partner why the proof still works after you do this. Record a summary of your conversation below.
Can vertical angles be obtuse angles? Acute angles? Right angles? If you need to, think back to all the vertical angles you made while adjusting slopes of lines above.
Are vertical angles always supplementary? Think about what happens when you double the different angle values you have seen in the activities above.
If both pairs of vertical angles had the same measure, what would the angle measure need to be?