How do you prove perpendicular line is the shortest distance?
Table of Contents
- 1 How do you prove perpendicular line is the shortest distance?
- 2 Is the shortest segment from a point to a line is the perpendicular segment from the point to the line?
- 3 What is the perpendicular distance of the point?
- 4 How do you find a perpendicular line segment?
- 5 How smallest line is perpendicular?
How do you prove perpendicular line is the shortest distance?
Given: XY is a straight line and O is a point outside it. OP is perpendicular to XY and OZ is an oblique. To Prove: OP < OZ….Perpendicular is the Shortest.
| Statement | Reason |
|---|---|
| 3. ∠OZP < ∠OPZ. | 3. From statement 1 and 2. |
| 4. OP < OZ. (proved) | 4. In a triangle, the greater angle has the greater side opposite to it. |
Is the shortest segment from a point to a line is the perpendicular segment from the point to the line?
The perpendicular bisector of a segment is a line perpendicular to a segment at the segment’s midpoint. The shortest segment from a point to a line is perpendicular to the line. This fact is used to define the distance from a point to a line as the length of the perpendicular segment from the point to the line.
Why are perpendicular lines the shortest?
Because its a straight line connecting the parallel lines at a 90-degree angle. | This is perpendicular to the parallel lines and is the shortest distance between them.
What is the perpendicular distance of the point?
In geometry, the perpendicular distance between two objects is the distance from one to the other, measured along a line that is perpendicular to one or both. Particular instances include: Distance from a point to a line, for the perpendicular distance from a point to a line in two-dimensional space.
How do you find a perpendicular line segment?
A straightforward way of finding a perpendicular bisector is to measure a line segment that you need to bisect. Then divide the measured length by two in order to find its midpoint. Draw a line out from this midpoint at a 90 degrees angle.
How do you find the perpendicular Pythagorean Theorem?
Here, ‘a’ is the perpendicular, ‘b’ is the base and ‘c’ is the hypotenuse. You can term ‘a’ and ‘b’ as the legs of that triangle which meet each other at 90°. Hence, the formula will be a2 + b2 = c2.
How smallest line is perpendicular?
These lines are said to be perpendicular if the angle formed by the 2 lines is 90 degrees. So, a perpendicular line is one that is at a 90 degree angle to another line.