Altitude and Orthocenter Construction
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This example demonstrates how to construct the altitudes of a triangle and locate the orthocenter in GeoGebra. The core mathematical concepts include the definition of altitude, the properties of the orthocenter, and the theorem that the three altitudes intersect at a single point. Construction details: Use Segment to construct triangle ABC's sides, Line and OrthogonalLine to draw perpendiculars from vertices to opposite sides, Intersect to find the intersection point (orthocenter), and Angle to verify angle relationships. Suitable for middle and high school geometry teaching, exploring orthocenter properties, and demonstrating altitude-related theorems.
GeoGebra Commands & Parameters
Segment(A, B) → aSegment(B, C) → bSegment(C, A) → cLine(C, A) → dLine(A, B) → eLine(B, C) → fOrthogonalLine(C, e) → gOrthogonalLine(B, d) → hOrthogonalLine(A, f) → iIntersect(f, i) → DSegment(D, B) → jIntersect(h, g) → EIntersect(d, h) → FAngle(A, F, B) → βSegment(F, A) → kAngle(C, D, A) → αIntersect(e, g) → GSegment(B, G) → lAngle(B, G, C) → γ