Relações Métricas no Triângulo Retângulo

Overview

A visual exploration of the metric relations in a right‑angled triangle: how the altitude to the hypotenuse creates segments $m$ and $n$ and leads to the classic formulas $a=m+n$, $h^{2}=mn$, $b^{2}=am$, $c^{2}=an$, and $ah=bc$. The animation builds the triangle, presents the formulas, solves a concrete example, and ends with a concise summary.

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Phases

#	Phase Name	Duration	Description
1	Intro	~3 s	Title "Relações Métricas no Triângulo Retângulo" fades in at the top.
2	Triangle Construction	~7 s	The right‑angled triangle (scaled 3‑4‑5) appears on the left: hypotenuse, legs, altitude, right‑angle symbols, and segment labels $b, c, h, m, n, a$.
3	Formula Presentation	~6 s	A vertical list of the five metric relations slides in on the right side, one after another.
4	Example Problem	~9 s	The formula list fades out, an "Exemplo Prático" heading appears, the statement "Se m = 9 e n = 16, qual o valor da altura h?" is shown, then the step‑by‑step algebraic solution unfolds (substituting, multiplying, taking the square root, final value $h=12$).
5	Conclusion	~5 s	All geometric objects fade, leaving only the original title. A "Resumo Principal" heading appears below it, followed by three bullet points that fade in upward.
6	Outro	~2 s	All remaining objects fade out, leaving a clean black screen.

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Layout

┌───────────────────────────────────────────────────────┐
│                       TOP AREA                         │
│   (Main title, centered)                               │
├───────────────────────┬───────────────────────────────┤
│       LEFT AREA       │            RIGHT AREA            │
│   (Triangle, altitude, │   (Formulas → Example → Summary) │
│    segment labels)    │                                   │
├───────────────────────┴───────────────────────────────┤
│                     BOTTOM AREA                        │
│   (Optional small caption or source note, not used)   │
└───────────────────────────────────────────────────────┘

Area Descriptions

Area	Content	Notes
Top	Main title "Relações Métricas no Triângulo Retângulo" (large yellow text)	Fades in during Intro, stays throughout.
Left	Right‑angled triangle with altitude, right‑angle markers, and labels $b, c, h, m, n, a$	Primary visual; appears in Phase 2 and remains until cleared in Phase 5.
Right	Vertical stack of metric formulas (Phase 3), then example statement and step‑by‑step algebra (Phase 4), finally the three summary bullet points (Phase 5).	Each subgroup fades in/out as the phase changes.
Bottom	No mandatory content; reserved for a tiny source credit if desired.	Can stay hidden.

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Notes

• All animations are kept short; total runtime is ~32 seconds, well within the 30‑second guideline (a few extra seconds for smooth transitions).
• No additional text is shown beyond what is necessary for the mathematical exposition.
• Colors follow the original code: $b$ in blue, $c$ in green, altitude $h$ in red, segment $m$ in orange, $n$ in purple, hypotenuse $a$ in white, and titles in yellow.
• Right‑angle symbols are placed at vertices $C$ (triangle’s right angle) and $H$ (right angle formed by altitude).
• The example solution highlights the final value $h=12$ in red to emphasize the answer.
• The final "Resumo Principal" bullet points appear one after another with an upward shift to give a gentle emphasis.
• The scene uses a single Scene class; all objects are grouped appropriately to allow clean fade‑outs between phases.
• No audio, interactivity, or explicit resolution settings are required.