How To Find The Length Of The Legs Of An Isosceles Triangle Using The Pythagorean Theorem

Legs of an isosceles triangle Chapter 5 (p. 244)

The two congruent sides of an isosceles triangle

An isosceles triangle is a triangle with two sides of equal length. The third side is called the base. In an isosceles triangle, the angles opposite to the equal sides are also equal.

To find the measure of the legs of an isosceles triangle, we can use the Pythagorean Theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

In an isosceles triangle, the two legs are equal in length, so we can label them as a and the base as b. We can then use the Pythagorean Theorem to solve for the length of the legs:

a^2 + b^2 = c^2

Since we know that the base is half the length of the hypotenuse (the third side) in an isosceles triangle, we can write:

a^2 + (b/2)^2 = c^2

We can also use the fact that the angle opposite to the base is equal to the two other angles in the triangle, and it can be divided into two equal parts by drawing a perpendicular line from the vertex to the base. This line will divide the base into two equal segments.

Using the Pythagorean Theorem, we can solve for the length of the legs of the isosceles triangle in terms of the length of the base:

a = sqrt(c^2 – (b/2)^2)

Thus, the length of the legs of an isosceles triangle can be found using the Pythagorean Theorem and the fact that the base is half the length of the hypotenuse.

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