Understanding 45-45-90 Triangles | Properties, Formulas, and Applications

Angles= 45-45-90; sides= 1-1-√(2)

Let’s start by understanding the concept of angles and sides in geometry

Let’s start by understanding the concept of angles and sides in geometry.

In geometry, an angle is formed by two rays that have a common endpoint, called the vertex. The two rays are called the sides of the angle. Angles are typically measured in degrees or radians. In this case, the given angles are 45-45-90.

A 45-45-90 triangle is a special type of right triangle where the two legs (the sides that form the right angle) are congruent in length, and the hypotenuse (the longest side opposite the right angle) is equal to the length of the legs multiplied by the square root of 2 (√2). So, the sides of a 45-45-90 triangle can be represented as 1-1-√(2).

To visualize this triangle, imagine a right triangle where each of the two legs has a length of 1 unit. Since the angles are both 45 degrees, the triangle will be an isosceles triangle with the two congruent sides forming the right angle. The hypotenuse can be found using the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, it becomes 1^2 + 1^2 = √(2)^2, which simplifies to 2 = 2. Therefore, the length of the hypotenuse is √(2).

In summary, a 45-45-90 triangle has two congruent legs, each measuring 1 unit, and a hypotenuse of √(2) units. The angles in this triangle are both 45 degrees.

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