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2.8 Similar Triangles are Proportional


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Last updated 26 October 2012 15:30 by NZTecAdmin

Get learners to draw a right triangle, any size they like, that has a 30° angle in it. Get them to compare their triangles and discuss what makes them all look similar.

Similar triangles are proportional. If one triangle has a hypotenuse twice as long as another triangle’s hypotenuse, then the other two sides of the larger triangle are also twice as long as the smaller triangles corresponding sides.

Get learners to measure their triangle’s longest side (hypotenuse) and shortest side (opposite the 30° angle). Record everyone’s pairs of measurements under the headings “side opposite 30°” and “hypotenuse”. Get them to generalise the relationship between the two sides. You’ll get a table similar to this one:

Student Side opposite 30° hypotenuse
1 22 mm 44mm
2 5 cm 10 cm
3 62 mm 124 mm

In a right triangle with a 30° (and 60°) angle, the hypotenuse is always twice the length of the side opposite 30°. Conversely, the side opposite 30° is ½ the length of the hypotenuse.

In fact, there is a fixed ratio between the side opposite any angle in a right triangle and the hypotenuse. This ratio is called sine.

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