Math Problem Statement
Solution
The question asks for a true statement about a 45°-45°-90° triangle, which is a special right triangle.
In a 45°-45°-90° triangle, the legs are congruent, and the hypotenuse is always √2 times the length of either leg. This is derived from the Pythagorean Theorem, where for such triangles, if each leg has length x, the hypotenuse has length x√2.
Thus, the correct answer is A: The hypotenuse is √2 times as long as either leg.
Would you like further details on how the properties of a 45°-45°-90° triangle are derived, or do you have other questions?
Here are some related questions for deeper understanding:
- How do we derive the relationship between the legs and hypotenuse in a 45°-45°-90° triangle?
- What is the Pythagorean Theorem, and how is it applied to right triangles?
- How do the side ratios differ between a 45°-45°-90° triangle and a 30°-60°-90° triangle?
- Can we use trigonometric functions to find angles in a 45°-45°-90° triangle?
- How can a 45°-45°-90° triangle be applied in real-world problems?
Tip: Always remember that in a 45°-45°-90° triangle, both legs are equal, and the hypotenuse is √2 times the length of a leg.
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Math Problem Analysis
Mathematical Concepts
Geometry
Special Right Triangles
Pythagorean Theorem
Formulas
Hypotenuse = Leg * √2
Theorems
Pythagorean Theorem
Suitable Grade Level
Grades 9-10