![]() ![]() We shall develop the four standard tests used to check that two triangles are congruent. Most of our discussion therefore concerns congruent triangles. ![]() (Pythagoras’ theorem gives us the answer 2 cm for this length.) This very simple idea of matching lengths, matching angles, and matching areas becomes the means by which we can prove many geometric results.Ī polygon can always be divided up into triangles, so that arguments about the congruence of polygons can almost always be reduced to arguments about congruent triangles. For example, if we measure or calculate the unmarked side length of the diagram on the left above, then the matching length is the same in the diagram on the right above. Knowing that two figures are congruent is important. On the other hand, the two figures below are exactly the same in all respects apart from their position and orientation − we can pick up one of them and place it so that it fits exactly on top of the other. For example, all the angles of the square and the rectangle below are right angles, and they have the same area, but their side lengths are different. Two geometric figures may resemble each other in some ways, but differ in others. ![]()
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