Right Prism in GeoGebra: Parametric Construction and Net
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This example demonstrates how to construct a right prism in GeoGebra, producing the 3D solid and its corresponding net (unfolding) with clear geometric annotations. The key mathematical ideas are the defining property of a right prism (lateral edges perpendicular to the base), the relationship between base polygons and lateral faces, and how these structures remain consistent under parameter changes. Construction highlights: it uses Prism to create the solid; Point, Polygon, and Segment to build and control the base and boundary edges; Intersect to locate vertices via geometric intersections for correct connectivity between faces; Rotate (and RotateText) to show rotations and maintain readable labels during view/expansion; Midpoint to assist with auxiliary points; Angle and Textfield to annotate angle relationships; and Net to generate the unfolding. The model is further controlled by input boxes (InputBox1/2/3) and parameter-driven objects (e.g., t1/t2, dimensions) for interactive exploration. Suitable for secondary school through early university, especially for solid geometry, geometric construction, and parametric visualization tasks.
GeoGebra Commands & Parameters
Intersect(xAxis, yAxis) → CTextfield(a) → InputBox1Textfield(b) → InputBox2Textfield(h) → InputBox3Point(Circle[D, 3]) → EPolygon(D, E, F) → t1, f, d, e_1Point(Circle[G, Segment[D, E]]) → HRotate(H + (Segment[E, F], 0), Angle[F - E] + Angle[H - G] - Angle[E - D], H) → IPolygon(G, H, I) → t2, i, g, h_1Intersect(d, e_1) → JIntersect(g, h_1) → KSegment(J, K) → jSegment(D, G) → kSegment(E, H) → lAngle(J, E, D) → αAngle(K, H, G) → βRotateText(text7, 45°) → text8RotateText(text5, 90°) → text9Midpoint(j) → LTextfield(m) → InputBox4Polygon(A, B, C) → t3, c_1, a_1, b_1Prism(t3, h) → e, M, edgeCO, edgeMN, edgeNO, edgeMO, N, O, faceABNM, faceBCON, faceACOM, faceMNO, edgeAM, edgeBNNet(e, p) → q, P, A_1, facePQR, facePQTS, faceQRVU, facePRWZ, face1, edgePQ, edgeQR, edgePR, edgePS, Q, edgeST, edgeQT, edgeQU, edgeUV, edgeRV, edgeRW, edgeWZ, edgePZ, edge2, edge1, R, S, T, U, V, W, Z
AI Drawing Prompt Reference
Draw a right prism as a 3D solid together with its net (unfolding). First, create a base polygon in the plane using the given base parameters, labeling the base vertices and boundary edges. Construct the top base by extending perpendicular lateral edges from the base so that the prism remains a right prism; connect the corresponding vertices to form the lateral faces. Use angle annotations to highlight key relationships between edges and maintain the correct connectivity as dimensions vary. Finally, unfold the prism into a net, showing the connected faces in the plane along with the matching vertices and border edges of the unfolding.
The prompt above was compiled from the original drawing commands and is for reference only.