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Vertical Angles Explorer

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About This MicroSim

This interactive demonstration allows you to rotate one of two intersecting lines and observe that vertical angles always remain equal, no matter how you rotate the lines.

Vertical Angles Theorem

When two lines intersect, vertical angles are congruent.

\[\angle 1 \cong \angle 3$$ $$\angle 2 \cong \angle 4\]

How to Use

  1. Drag either blue endpoint to rotate the line
  2. Watch all four angle measures update in real-time
  3. Notice that opposite angles (vertical angles) always match
  4. Observe that adjacent angles always sum to 180°

Color Coding

Color Angles Relationship
Green ∠1 and ∠3 Vertical (equal)
Yellow ∠2 and ∠4 Vertical (equal)

Key Observations

  • Vertical angles are always congruent
  • Adjacent angles are always supplementary (sum to 180°)
  • This works for any rotation of the lines

Learning Objectives

  • Discover that vertical angles are always congruent
  • Apply the vertical angles theorem
  • Analyze the relationship between all four angles

Bloom's Taxonomy Level

Analyzing - Discovering patterns through manipulation.

Iframe Embed Code

<iframe src="https://dmccreary.github.io/geometry-course/sims/vertical-angles-explorer/main.html"
        height="552px"
        width="100%"
        scrolling="no"></iframe>