Triangle Angle Sum Proof with Parallel Line

Overview

A concise visual proof that the interior angles of any triangle sum to $180^\circ$ by extending one side and drawing a parallel line to illustrate the relationship between interior and exterior angles.

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Phases

#	Phase Name	Duration	Description
1	Intro	~3s	Title fades in, then the triangle appears centered on the screen.
2	Extend Base & Parallel Line	~6s	The base of the triangle is extended left and right; a line parallel to the opposite side is drawn through the left extension point.
3	Angle Correspondence	~8s	Highlight the interior angles of the triangle and the corresponding alternate interior angles formed with the parallel line, showing they are equal. Ensure angle arcs are drawn correctly at each vertex, with proper orientation and positioning to accurately represent each angle.
4	Sum Demonstration	~5s	Animate the three angles (two interior + one exterior) aligning along the parallel line to visually sum to a straight angle ($180^\circ$). Verify that the angle markers maintain their correct orientation and size during the alignment animation.
5	Outro	~3s	Fade out the construction, leaving only the statement "$\angle A + \angle B + \angle C = 180^\circ$" centered.

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Layout

┌─────────────────────────────────────────────┐
│                 TOP AREA                    │
├───────────────────────┬─────────────────────┤
│                       │                     │
│      MAIN AREA        │   (optional)        │
│   (triangle + line)   │   supporting note   │
│                       │   (e.g., "Alt. int.")│
├───────────────────────┴─────────────────────┤
│                 BOTTOM AREA                 │
└─────────────────────────────────────────────┘

Area Descriptions

Area	Content	Notes
Top	Title "Triangle Angle Sum Proof"	Fades in during Intro
Main	Geometric construction: triangle $ABC$, extended base $AB$, parallel line through extension point, angle highlights	Central visual focus throughout phases
(optional) Right	Small label indicating "Alternate interior angles" when those are highlighted	Appears only in Phase 3
Bottom	Final equation $\angle A + \angle B + \angle C = 180^\circ$	Appears in Outro

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Assets & Dependencies

• Angle Markers: Use Manim's Angle class to create accurate angle arcs at each vertex
  • Each angle marker must be positioned at the correct vertex
  • The arc should span between the two rays forming the angle
  • Use appropriate radius (suggested: 0.5 units) for visibility
  • Ensure the arc direction follows the interior angle, not the exterior
• Color Coding: Assign distinct colors to each of the three angles (e.g., RED for angle A, GREEN for angle B, BLUE for angle C) and maintain consistency throughout all phases
• Angle Labels: Optional small labels ($\alpha$, $\beta$, $\gamma$ or A, B, C) positioned near each angle arc

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Notes

• All drawing actions (lines, extensions, highlights) should be smooth linear animations to keep total runtime under 30 seconds.
• Use consistent colors: triangle edges in a neutral color, highlighted angles in bright contrasting colors (e.g., red, green, blue).
• Angle Marking Requirements:
  • Each angle must be marked with an arc that clearly shows the interior angle at each vertex
  • The arc should be drawn from one side of the angle to the other, centered at the vertex
  • When showing alternate interior angles, ensure the corresponding angles on the parallel line have matching arc sizes and orientations
  • Double-check that angle arcs do not overlap with triangle edges in a confusing way
• When aligning angles along the parallel line for the sum, animate them sliding into place to form a straight line, reinforcing the $180^\circ$ result. Ensure angle markers remain properly oriented and sized during this transformation.
• No textual narration is required; visual cues and brief on‑screen labels suffice.
• The entire animation fits within a single Manim Scene class.