
Altitude on Hypotenuse
Flashcard
•
Mathematics
•
9th - 12th Grade
•
Practice Problem
•
Hard
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15 questions
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1.
FLASHCARD QUESTION
Front
What is the altitude on the hypotenuse in a right triangle?
Back
The altitude on the hypotenuse is a line segment drawn from the right angle to the hypotenuse, forming two smaller right triangles that are similar to the original triangle.
2.
FLASHCARD QUESTION
Front
How do you calculate the area of a triangle using the altitude?
Back
Area = 1/2 * base * height, where the base is the length of the hypotenuse and the height is the length of the altitude.
3.
FLASHCARD QUESTION
Front
What is the relationship between the altitude and the segments it creates on the hypotenuse?
Back
The altitude divides the hypotenuse into two segments, and the product of the lengths of these segments is equal to the square of the length of the altitude.
4.
FLASHCARD QUESTION
Front
If the hypotenuse is 10 units and the altitude is 6 units, what are the lengths of the segments on the hypotenuse?
Back
Let the segments be x and y. Then, x * y = 6^2 = 36. The sum of x and y must equal 10. Solve the equations to find x and y.
5.
FLASHCARD QUESTION
Front
What is the geometric mean in relation to the altitude on the hypotenuse?
Back
The length of the altitude is the geometric mean of the lengths of the two segments it creates on the hypotenuse.
6.
FLASHCARD QUESTION
Front
If the segments on the hypotenuse are 4 units and 6 units, what is the length of the altitude?
Back
The altitude can be found using the formula: altitude = √(4 * 6) = √24 = 2√6.
7.
FLASHCARD QUESTION
Front
What is the Pythagorean theorem?
Back
In a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): c² = a² + b².
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