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Obtuse isosceles triangle image1/21/2024 ![]() In our last triangle, none of the sides have the same length, so this is called a scalene triangle. It’s a hard one to spell, but an easy one to recognize! Scalene Triangle ![]() When two of the sides of a triangle are the same it’s called an isosceles triangle. In the middle triangle, we can see that two of the sides are the same length and measure 8 cm while the third is 9 cm. It’s not too tough of a name to remember since the beginning of equilateral sounds like the word equal, and the word lateral means “side.” Isosceles Triangle A triangle like this one where all the sides are the same is called an equilateral triangle. In the triangle on the left, we can see that all three sides are the same length and measure 9 centimeters. Here are three triangles with the lengths of the sides included: Our second set of triangles is categorized by how many of the sides have the same length. That’s all there is to it for these three types! We just find the largest angle and the name of the triangle will correspond to the name of that angle. Because this is more than 90 degrees, this is an obtuse angle, so we call this triangle an obtuse triangle. Obtuse Triangleįinally, in the triangle on the right, the largest angle is 117 degrees. You might remember that a 90-degree angle is a right angle, so this triangle is a right triangle. We can see that in the middle triangle the largest angle is exactly 90 degrees. This one is easy to remember, since “cute” things are often small, like puppies and kittens. Just remember that acute angles are less than 90 degrees. 70 is less than 90, so this is an acute triangle. We can see that the largest angle in the triangle on the left is 70 degrees. These are the acute, right, and obtuse triangles.īut how do you know which is which? Take a look at the largest angle of each triangle and note whether or not the angle is more than, less than, or equal to 90 degrees. Let’s start with the three types of triangles that are categorized by the measure of their largest angle. We’re going to break our six types of triangles into two groups of three. This is true for all triangles, including the six types we’re looking at today. In addition, a triangle has three interior angles, and the sum of those three angles is always 180 degrees. ![]() ![]() The length of the sides can vary but the length of the largest side can’t be equal or greater to the sum of the other two sides. By working through everything above, we have proven true the converse (opposite) of the Isosceles Triangle Theorem.Hi, and welcome to this review of different types of triangles! Before we begin, here’s a review of the basics.Ī triangle has three straight sides that connect. When the triangles are proven to be congruent, the parts of the triangles are also congruent making EF congruent with EH. That gives us two angles and a side, which is the AAS theorem. We now have what’s known as the Angle Angle Side Theorem, or AAS Theorem, which states that two triangles are equal if two sides and the angle between them are equal. 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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