Similarity, Congruence & Scale Factor
Explore proportional geometry. Visualize shadow magnification, similar triangle scale ratios, and matching congruence theorems.
Proportional Projection
Shadow Projector Simulator
Similar figures possess matching angles and proportional side lengths. By projecting light rays past a vertical object, we construct two nested similar triangles sharing equal coordinate ratios: H_shadow / H_object = D_shadow / D_object.
Proportional Ratios
Ratio: 120 / 60 = 2.0x (Scale Factor)
Similarity Mathematical Proof:
Similar Triangles: ΔLOB (Light-Object) ~ ΔLSD (Light-Screen).
Scale Factor: s = (d1 + d2) / d1 = 2.00
Shadow Height: H_shadow = s × H_object = 120.0 px
Scale Factor: s = (d1 + d2) / d1 = 2.00
Shadow Height: H_shadow = s × H_object = 120.0 px
Geometric Theorems
Congruence Criteria Proofs
Congruence means figures share exact side lengths and angle sizes. Select a congruence criteria tab below to highlight corresponding matching parameters on our triangle pair.
Criteria Definition
SSS: Side-Side-Side
Matching Parts Log:
If three sides of one triangle are equal to three sides of another triangle, the triangles are proven congruent.
- Side AB = A'B' (Cyan tick)
- Side BC = B'C' (Green tick)
- Side CA = C'A' (Yellow tick)
- Side AB = A'B' (Cyan tick)
- Side BC = B'C' (Green tick)
- Side CA = C'A' (Yellow tick)
Self Evaluation
Scaling & Congruence Quiz
Test your understanding of similarity ratios, congruence proofs, and dimensions scaling.
Question 1 of 5
Score: 0/0
If two shapes are SIMILAR but not congruent, which of the following is true?
Correct Answer!
Explanation goes here.
Focus Area Vocabulary
- Similarity (∼): Equal angles, scaled sides
- Congruence (≅): Equal angles, equal sides
- Scale Factor (s): Proportion multiplier