HKCEE MC #3
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This example illustrates the properties of similar triangles. Key mathematical concepts include the criteria and properties of similar triangles. Using the construction of triangle medians, coordinate systems, and circle properties, the example demonstrates the proportional relationships between corresponding sides of similar triangles. GeoGebra commands used include objects a, b, text1, text2, text3, text4, g, h, i, j, f, and text5. Suitable for middle school students learning about similar triangles.
GeoGebra Commands & Parameters
Numeric a(2.0)Numeric b(2.0)Line g(1.0, 0.0, -1.5707963267948966)Line h(1.0, 0.0, -3.141592653589793)Line i(1.0, 0.0, -4.71238898038469)Line j(1.0, 0.0, -6.283185307179586)f(x) = If[0 ≤ x ≤ 6.28319,(a * sin((b * x)))]
AI Drawing Prompt Reference
Draw two similar right triangles, with one triangle having legs of length 2 and 2. The other triangle is obtained by scaling the first one. Use the properties of triangle medians, coordinate systems, and circles to demonstrate the proportional relationships between corresponding sides of similar triangles. First, draw the x-axis, then draw three horizontal lines parallel to the x-axis, and finally draw a sine curve f(x) = a * sin(b * x) with a and b both set to 2.
The prompt above was compiled from the original drawing commands and is for reference only.