Question

Prove that shortest line from a point on a straight line is perpendicular to the line or vice-versa.​

Answer 1

Answer:

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.

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Perpendicular is the Shortest.

Step-by-step explanation:

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Answer 2

Answer:

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.

Perpendicular is the Shortest

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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.

Step-by-step explanation:

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