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Step 1:: Understand the concept of a 45 - 45 - 90 triangle
This triangle has equal leg lengths and a hypotenuse that is longer than the legs by a factor of $\sqrt{2}$.
A 45 - 45 - 90 triangle is a special right triangle where the angles are 45 degrees, 45 degrees, and 90 degrees.
Step 2:: State the 45 - 45 - 90 triangle rule
This means that for any 45-45-90 triangle, the length of the hypotenuse is always $\sqrt{2}$ times longer than the length of a leg.
Step 3:: Derive the 45 - 45 - 90 triangle rule
l : h = 1 : \sqrt{2}
In a right triangle, the Pythagorean theorem states that: Since a 45 - 45 - 90 triangle has equal legs, we can write: Now, the Pythagorean theorem becomes: So, the ratio of the leg length to the hypotenuse length is:
Final Answer
The 45 - 45 - 90 triangle rule states that the ratio of the leg length to the hypotenuse length in a 45 - 45 - 90 triangle is 1 : $\sqrt{2}$. This means that for any 45 - 45 - 90 triangle, the length of the hypotenuse is always $\sqrt{2}$ times longer than the length of a leg.
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