Legs of an isosceles triangle Chapter 5 (p. 244)
The two congruent sides of an isosceles triangle
An isosceles triangle is a special type of triangle in which two sides are of equal length. Due to this, the opposite angles of those sides are also equal. Therefore, if we label the length of those two sides as a and the length of the remaining side as b, then we can say that:
a = b,
and the opposite angles of those sides are also equal, which means that:
angle A = angle B.
To find the length of the remaining side, we can use the Pythagorean theorem, which states that:
c^2 = a^2 + b^2,
where c is the length of the hypotenuse of a right-angled triangle formed by the isosceles triangle.
Since our isosceles triangle has two sides of equal length, we can simplify the above equation as follows:
c^2 = a^2 + a^2
c^2 = 2a^2
c = sqrt(2a^2)
c = a * sqrt(2)
Therefore, the length of the remaining side of an isosceles triangle with two sides of length a is:
b = a * sqrt(2)
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