Two Types of Perpendicular Constructions

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About This Diagram

This comparison shows the two types of perpendicular constructions: 1. Through a point ON the line - Point P is on line ℓ 2. From a point TO the line - Point P is not on line ℓ

Hover over each panel to see the construction steps.

Key Differences

Type	Given	Goal
ON Line	Point P is on ℓ	Construct line through P perpendicular to ℓ
TO Line	Point P is off ℓ	Construct line from P perpendicular to ℓ

When to Use Each

• ON Line: When you need a perpendicular at a specific point on a line
• TO Line: When you need the shortest distance from a point to a line

How to Use

1. Hover over the left panel to see "perpendicular through point ON line"
2. Hover over the right panel to see "perpendicular from point TO line"
3. Compare the steps listed below each diagram

Learning Objectives

• Distinguish between the two perpendicular construction methods
• Apply the appropriate construction based on point location
• Analyze why each construction produces a perpendicular

Bloom's Taxonomy Level

Understanding, Applying, and Analyzing - Distinguishing and applying constructions.

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