![]() Because we have an angle bisector with the line segment EG, FEG is congruent with HEG. Label this point on the base as G.īy doing this, we have made two right triangles, EFG and EGH. To do that, draw a line from FEH (E is the apex angle) to the base FH. We need to prove that EF is congruent with EH. The EFH angle is congruent with the EHF angle. It states, “if two angles of a triangle are congruent, the sides opposite to these angles are congruent.” Let’s work through it.įirst, we’ll need another isosceles triangle, EFH. They are visible on flags, heraldry, and in religious symbols.Īs with most mathematical theorems, there is a reverse of the Isosceles Triangle Theorem (usually referred to as the converse). You can also see isosceles triangles in the work of artists and designers going back to the Neolithic era. In the Middle Ages, architects used what is called the Egyptian isosceles triangle, or an acute isosceles triangle. Ancient Greeks used obtuse isosceles triangles as the shapes of gables and pediments. Ancient Egyptians used them to create pyramids. Īs far as isosceles triangles, you see them in architecture, from ancient to modern. You can also see triangular building designs in Norway, the Flatiron Building in New York, public buildings and colleges, and modern home designs. The triangular shape could withstand earthquake forces, unlike a rectangular or square design. In 1989, Japanese architects decided that a triangular building design would be necessary if they were to construct a 500-story building in Tokyo. With modern technology, triangles are easier to incorporate into building designs and are becoming more prevalent as a result. While rectangles are more prevalent in architecture because they are easy to stack and organize, triangles provide more strength. ![]()
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