Theorems About Perpendicular Lines
1. Shortest Distance from a Point to a Line
The distance from a point to a line is the length of the perpendicular segment from the point to the line. This perpendicular segment is the shortest distance between the point and the line.
![Shortest distance from a point to a line](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-2310.png)
2. Shortest Distance Between Two Parallel Lines
The distance between two parallel lines is the length of any perpendicular segment joining the two lines.
![Shortest distance between two parallel lines](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-2302.png)
3. Perpendicular Transversal Theorem
If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other.
![Perpendicular transversal theorem](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-2303.png)
4. Lines Perpendicular to a Transversal Theorem
In a plane, if two lines are perpendicular to the same line, then they are parallel to each other.
![Lines perpendicular to a transversal theorem](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-2311.png)
5. Theorem
If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular.
![Theorem 1](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-2305.png)
6. Theorem
If two lines are perpendicular, then they intersect to form four right angles.
![Theorem 2](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-2304-995x1024.png)
7. Theorem
If two sides of two adjacent acute angles are perpendicular, then the angles are complementary.
![Theorem 3](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/2-6-1024x902.png)
Exercise
- Find m∠1.
![Find m∠1.](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-2312.png)
- In the diagram, , (FG) ⊥ (GH) Find the value of
![In the diagram, , (FG) ⊥ (GH) Find the value of](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-2315.png)
- Determine which lines, if any, must be parallel. Explain your reasoning.
![Determine which lines, if any, must be parallel. Explain your reasoning.](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-2317.png)
- Find all the unknown angle measures in the diagram at the right. Justify your reasoning for each angle measure.
![Find all the unknown angle measures in the diagram at the right. Justify your reasoning for each angle measure.](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-2318.png)
- Find all the unknown angle measures in the diagram at the right. Justify your reasoning for each angle measure.
![Find all the unknown angle measures in the diagram at the right. Justify your reasoning for each angle measure.](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-2319.png)
Concept Map
![Concept Map](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-2309-1024x482.png)
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