Indirect Proof Explorer

About This MicroSim

This interactive visualization guides students through the four stages of indirect proof (proof by contradiction). Choose from multiple geometry examples and step through each stage to understand how assuming the opposite leads to a contradiction.

The Four Stages

ASSUME OPPOSITE - Negate what you want to prove
DERIVE CONSEQUENCES - Follow the logical implications
FIND CONTRADICTION - Discover the clash with known truths
CONCLUDE TRUTH - The original statement must be true

How to Use

Select a proof from the dropdown menu
Click Next Stage to reveal each part of the proof
Observe how each stage builds on the previous one
Notice the contradiction that emerges in stage 3
Use Reset to start over with a new proof

Available Proofs

Lines intersect at one point - Classic intersection uniqueness
Isosceles triangle base angles - Equal sides mean equal angles
Parallel lines alternate angles - Transversal angle relationships

Interactive Features

Stage-by-stage reveal - See the proof unfold logically
Multiple examples - Compare different indirect proofs
Visual highlighting - Current stage glows for emphasis
Color-coded stages - Each stage has a distinct color

Why Indirect Proof?

Some statements are easier to prove by contradiction:

Assume the opposite is true
Show this leads to an impossibility
Conclude the original statement must be true

Learning Objectives

Construct indirect proofs by identifying assumptions
Derive consequences from assumed statements
Identify contradictions with known postulates/theorems
Evaluate when indirect proof is appropriate

Bloom's Taxonomy Level

Evaluating - Constructing indirect proofs requires evaluating logical consequences.

Iframe Embed Code

<iframe src="https://dmccreary.github.io/geometry-course/sims/indirect-proof-explorer/main.html"
        height="602px"
        width="100%"
        scrolling="no"></iframe>

References

Proof by Contradiction - Khan Academy