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SIMILAR POLYGONS |
| Geometry | |
| 1. SIMILAR TRIANGLES | |
| Two triangles are similar when their angles are equal and their sides are in the same ratio. In other words, if triangles ABC and A'B'C' are similar then A=A', B=B' and C=C', and the ratio values A'B'/AB=B'C'/BC=C'A'/CA=r, which is known as the ratio of similitude. | |
| 1.- Change the shape and
size of the green triangle in the Descartes window and watch how the
blue triangle, which is similar to the green triangle, changes too.
2.- If the sides of the green triangles were 3, 4 and 5 what would be the length of the sides of the blue one? 3.- Alter the ratio until its value is 1 and you will see that the triangles are identical in size and shape. 4.-Reduce the ratio to 0.5 and compare the triangles. How long are the sides of the green triangle if the sides of the blue triangle are 3, 5 and 7?
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5.- Repeat the process for ratios of 1.5, 0.25 and 3. Change the scale to 16 in the last example so that you can see both triangles. 6.- Are two equal triangles similar? What about two equilateral triangles? 7.- Are two triangles similar if their angles are equal? Are two triangles similar if their sides are in the same ratio? |
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| 2. SIMILAR POLYGONS | |
| Two polygons are similar if their angles are equal and their sides are in the same ratio. In other words, if polygons ABCDE and A'B'C'D'E' are similar then angles: A=A', B=B', C=C', D=D' and E=E', and the ratio values A'B'/AB=B'C'/BC=C'D'/CD=D'E'/DE=E'A'/EA=r, which is known as the ratio of similitude. | |
| 8.-
Change the shape and size of the green pentagon in the Descartes window
and watch how the blue pentagon changes shape so that it is always similar
to the green one. If the sides of the green pentagon measure 3, 4, 4, 6
and 6.5 what do the sides of the blue one measure?
9.- Change the ratio to 1 and note that the pentagons are identical in size and shape. Change the ratio to 2 and compare the pentagons. What are the measurements of the green pentagon if the sides of the blue one are 3, 5, 6, 8 and 7?
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10.- Repeat the process for ratios of 2, 3 and 0.25. Change the scale to 16 in the last example so that you can see both pentagons. 11.- Are two equal pentagons similar? What about two regular pentagons? Are two pentagons similar if their angles are equal? Are two pentagons similar if their sides are in the same ratio? |
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| Miguel García Reyes | ||
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| Spanish Ministry of Education. Year 2001 | ||
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