if base legs of an isosceles triangle are equal

Hence, the measure of the other two angles of an isosceles triangle is 55°. If we are given the measure of an unequal angle, we can simply calculate the other two angles using the angle sum property.Įxample: Let the measure of the unequal angle is 70° and the other two equal angles measures x, then as per angle sum rule, As a result, one of the angles is unbalanced. Two of the isosceles triangle's three angles are equal in measure, which is the polar opposite of the equal sides. As a result, we may employ Pythagoras theorem, which states that the square of the hypotenuse equals the sum of the squares of the base and perpendicular. The hypotenuse is the third unequal side of the triangle. Parts of a triangle Isosceles right triangleĪ right isosceles triangle has two equal sides, one of which serves as the perpendicular and the other as the triangle's base. If the two angles opposing the legs are equal and smaller than 90 degrees, the isosceles triangle is called an acute isosceles triangle. The isosceles triangle is classed as acute, right, or obtuse depending on the angle between the two legs. The perpendicular bisector of the base of every isosceles triangle has a symmetry axis. Legs, base, and height are the three dimensions of a triangle, as we all know. Types of Isosceles Triangle Isosceles acute triangle By working through everything above, we have proven true the converse (opposite) of the Isosceles Triangle Theorem.In general, the isosceles triangle may be divided into three types: 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.

If base legs of an isosceles triangle are equal