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The median on the hypotenuse of an isosceles right triangle is a line segment joining the midpoint of the hypotenuse to its opposite vertex. In an isosceles right triangle, this median has a special relationship with the legs of the triangle.
The calculator uses the formula:
Where:
Explanation: In an isosceles right triangle, the median to the hypotenuse is equal to half the length of the hypotenuse. Since the hypotenuse equals \( Legs \times \sqrt{2} \), the median becomes \( \frac{Legs \times \sqrt{2}}{2} = \frac{Legs}{\sqrt{2}} \).
Details: Calculating the median on the hypotenuse is important in geometry for understanding triangle properties, solving construction problems, and analyzing spatial relationships in right triangles.
Tips: Enter the length of the legs of the isosceles right triangle in meters. The value must be positive and greater than zero.
Q1: What is an isosceles right triangle?
A: An isosceles right triangle is a right triangle with two equal legs and angles of 45°, 45°, and 90°.
Q2: Why is the median on hypotenuse equal to legs/√2?
A: Because the hypotenuse equals legs × √2, and the median to hypotenuse is half of the hypotenuse, so median = (legs × √2)/2 = legs/√2.
Q3: Can this formula be used for any right triangle?
A: No, this specific formula applies only to isosceles right triangles where both legs are equal.
Q4: What are the properties of the median in a right triangle?
A: In any right triangle, the median to the hypotenuse equals half the length of the hypotenuse.
Q5: How is this different from the altitude to the hypotenuse?
A: The median connects the midpoint to the vertex, while the altitude is perpendicular to the hypotenuse from the opposite vertex. They are different line segments with different properties.