Dropping the altitude onto the hypotenuse makes two smaller triangles, both the same shape as the original. Matching up their sides is where the geometric mean comes from.
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The altitude to the hypotenuse of a right triangle splits the hypotenuse into segments of 8 and 13. Find the leg next to the segment of 8.
The altitude to the hypotenuse of a right triangle splits the hypotenuse into segments of 7 and 18. Find the leg next to the segment of 7.
The altitude to the hypotenuse of a right triangle splits the hypotenuse into segments of 13 and 21. Find the leg next to the segment of 13.
The altitude to the hypotenuse of a right triangle splits the hypotenuse into segments of 3 and 21. Find the leg next to the segment of 3.
The altitude to the hypotenuse of a right triangle splits the hypotenuse into segments of 15 and 9. Find the leg next to the segment of 15.
The altitude to the hypotenuse of a right triangle splits the hypotenuse into segments of 9 and 3. Find the leg next to the segment of 9.
The altitude to the hypotenuse of a right triangle splits the hypotenuse into segments of 10 and 17. Find the leg next to the segment of 10.
Find the other hypotenuse segment
In a right triangle a leg of length 12 meets the hypotenuse, and the altitude cuts off a segment of 9 next to that leg. Find the other segment of the hypotenuse.
The altitude to the hypotenuse of a right triangle is 3, and one segment of the hypotenuse is 1. Find the other segment.
The altitude to the hypotenuse of a right triangle is 4, and one segment of the hypotenuse is 2. Find the other segment.
In a right triangle a leg of length 14 meets the hypotenuse, and the altitude cuts off a segment of 7 next to that leg. Find the other segment of the hypotenuse.
The altitude to the hypotenuse of a right triangle is 5, and one segment of the hypotenuse is 25. Find the other segment.
In a right triangle a leg of length 5 meets the hypotenuse, and the altitude cuts off a segment of 1 next to that leg. Find the other segment of the hypotenuse.
The altitude is drawn to the hypotenuse. Find x.25
Find a leg or the hypotenuse
The altitude to the hypotenuse of a right triangle splits the hypotenuse into segments of 8 and 13. Find the leg next to the segment of 8.242
The altitude to the hypotenuse of a right triangle splits the hypotenuse into segments of 7 and 18. Find the leg next to the segment of 7.57
The altitude to the hypotenuse of a right triangle splits the hypotenuse into segments of 13 and 21. Find the leg next to the segment of 13.442
The altitude to the hypotenuse of a right triangle splits the hypotenuse into segments of 3 and 21. Find the leg next to the segment of 3.62
The altitude to the hypotenuse of a right triangle splits the hypotenuse into segments of 15 and 9. Find the leg next to the segment of 15.610
The altitude to the hypotenuse of a right triangle splits the hypotenuse into segments of 9 and 3. Find the leg next to the segment of 9.63
The altitude to the hypotenuse of a right triangle splits the hypotenuse into segments of 10 and 17. Find the leg next to the segment of 10.330
Find the other hypotenuse segment
In a right triangle a leg of length 12 meets the hypotenuse, and the altitude cuts off a segment of 9 next to that leg. Find the other segment of the hypotenuse.7
The altitude to the hypotenuse of a right triangle is 3, and one segment of the hypotenuse is 1. Find the other segment.9
The altitude to the hypotenuse of a right triangle is 4, and one segment of the hypotenuse is 2. Find the other segment.8
In a right triangle a leg of length 14 meets the hypotenuse, and the altitude cuts off a segment of 7 next to that leg. Find the other segment of the hypotenuse.21
The altitude to the hypotenuse of a right triangle is 5, and one segment of the hypotenuse is 25. Find the other segment.1
In a right triangle a leg of length 5 meets the hypotenuse, and the altitude cuts off a segment of 1 next to that leg. Find the other segment of the hypotenuse.24
Averaging the two pieces instead of multiplying them. The geometric mean is a square root of a product, and the ordinary average gives a different, wrong number every time the pieces differ.
Also called altitude to the hypotenuse or mean proportional.
What you can put on this worksheet
The geometric mean in a right triangle
The altitude is drawn to the hypotenuse. Find x.— a right triangle with the altitude drawn to its hypotenuse, labeled x, 9, 12→ 16
The leg rule
The altitude to the hypotenuse of a right triangle splits the hypotenuse into segments of 2 and 16. Find the leg next to the segment of 2.→ 6
The other hypotenuse segment
The altitude to the hypotenuse of a right triangle is 5, and one segment of the hypotenuse is 25. Find the other segment.→ 1
Altitude drawn: radicals, legs from the whole, two steps
Find x.— a right triangle with the altitude drawn to its hypotenuse, labeled 2, x, 4→ 10
Questions about these worksheets
Yes. Every similar right triangles sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.
Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.
Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.
Geometry is usually taken around 9th or 10th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.
Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.
That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the similar right triangles questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.
Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.
You pick from 4: the geometric mean in a right triangle, the leg rule, the other hypotenuse segment and altitude drawn: radicals, legs from the whole, two steps. Tick as many as you want and set how many of each, or let it spread them evenly.
Averaging the two pieces instead of multiplying them. The geometric mean is a square root of a product, and the ordinary average gives a different, wrong number every time the pieces differ.