Theorems About Perpendicular Lines
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.
2. Shortest Distance Between Two Parallel Lines
The distance between two parallel lines is the length of any perpendicular segment joining the two lines.
3. Perpendicular Transversal Theorem
If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other.
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.
5. Theorem
If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular.
6. Theorem
If two lines are perpendicular, then they intersect to form four right angles.
7. Theorem
If two sides of two adjacent acute angles are perpendicular, then the angles are complementary.
Exercise
- Find m∠1.
- In the diagram, , (FG) ⊥ (GH) Find the value of
- Determine which lines, if any, must be parallel. Explain your reasoning.
- 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.
Concept Map
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