Design tasks
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1) What is the point of construction problems? 2) Distinction between positional and non-positional problems 3) Procedure for solving construction problems (+ what each point means, what to look out for, ...) analysis writing down the construction process construction test conclusion (or discussion) 4) Sets of points given properties 5) Example 1 (triangle): Given a line segment AB of length 7 cm. Construct all triangles ABC for which additionally: α = 70°, b = 5 cm. basic example (we are rather analyzing the individual steps of the general procedure), positional problem analysis writing down the construction process "construction" (freehand) conclusion 6) Example 2 (triangle): Construct all triangles ABC for which c = 6 cm, vc = 1.5 cm, γ = 120°. example focused on demonstrating construction in GeoGebra and the use of circular arcs, non-positional problem analysis writing the construction procedure construction (in GeoGebra) conclusion 7) Example 3 (triangle): Given a line segment AB with a length of 5.6 cm. Construct all triangles ABC for which tc = 6 cm, tb = 4.5 cm also holds. more difficult example focused on demonstrating the use of the center of gravity and the properties of medians in construction, positional problem analysis writing the construction procedure "conclusion" (by estimation) 8) Example 4 (triangle): Given a line segment AB such that AB = 6 cm. Construct all triangles ABC, if va = 4 cm, tc = 4 cm. example focused on demonstrating that sometimes using a ray instead of a straight line can lead to a loss of solution, positional problem analysis writing the construction procedure construction (in GeoGebra) conclusion (in GeoGebra) 9) Construction problems for quadrilaterals, how to do it? differences from construction problems for triangles 10) Example 1 (quadrilateral): Construct a quadrilateral ABCD, if a = 6.5 cm, α = 60°, γ = 90°, δ = 105°, e = 8 cm. basic example with an example that if we only lack the size of one interior angle, we can (rather have to) calculate the size of the last one, non-positional problem analysis writing the construction procedure 11) Example 2 (trapezoid): Construct a trapezoid ABCD, if given: b = 4 cm, v = 3.5 cm, e = 8 cm, f = 7 cm. example with an example that sometimes we have to start with an unconventional line, non-positional problem analysis writing the construction procedure construction (in GeoGebra) test (in GeoGebra) conclusion (in GeoGebra) 12) Summary
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