Here we will prove that of all the straight lines that can be drawn to a straight line from a given point outside it, the perpendicular is the shortest.
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.
Proof:
Statement |
Reason |
1. In ∆OPZ, ∠OPZ = 90°. |
1. OP ⊥ XY. |
2. ∠OZP is an acute angle. |
2. In a triangle, if one angle is a right angle, the other two must be acute. |
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. |
From Perpendicular is the Shortest to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
Dec 03, 24 01:29 AM
Dec 03, 24 01:19 AM
Dec 02, 24 01:47 PM
Dec 02, 24 01:26 PM
Nov 29, 24 01:26 AM
New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.