Deciding whether a triangle has a right angle

Difficulty Stretch · Set jm1glc

Answer each one yes or no.

Fill in what you can and press Check. Nothing you type is sent anywhere.

1
A triangle has sides 10, 24 and 26. Is it a right triangle?
2
A triangle has sides 3, 4 and 3. Is it a right triangle?
3
A triangle has sides 7, 24 and 25. Is it a right triangle?
4
A triangle has sides 9, 40 and 39. Is it a right triangle?
5
A triangle has sides 3, 4 and 5. Is it a right triangle?
6
A triangle has sides 10, 24 and 28. Is it a right triangle?
7
A triangle has sides 8, 15 and 15. Is it a right triangle?
8
A triangle has sides 3, 4 and 5. Is it a right triangle?
9
A triangle has sides 3, 4 and 5. Is it a right triangle?
10
A triangle has sides 5, 12 and 13. Is it a right triangle?
11
A triangle has sides 10, 24 and 25. Is it a right triangle?
12
A triangle has sides 6, 8 and 10. Is it a right triangle?
13
A triangle has sides 16, 30 and 34. Is it a right triangle?
14
A triangle has sides 10, 24 and 26. Is it a right triangle?
15
A triangle has sides 10, 24 and 24. Is it a right triangle?
16
A triangle has sides 20, 21 and 29. Is it a right triangle?
17
A triangle has sides 7, 24 and 25. Is it a right triangle?
18
A triangle has sides 20, 21 and 29. Is it a right triangle?
19
A triangle has sides 9, 40 and 39. Is it a right triangle?
20
A triangle has sides 6, 8 and 8. Is it a right triangle?

What is in this set

The numbers in this set run from 3 to 43.
51% of them turn out to have a right angle.
49% of them turn out not to have a right angle.
A careful solution takes 3 written steps on average.
The mistake this set invites most often, in 100% of the problems: square the two shorter sides and add them.
Answers are a short answer exactly as the problem asks for it.

Drawing 240 problems from this page produced 57 different ones, 24% — so a sheet of 20 will come back to a problem you have seen — there are only so many sensible ones of this kind.

The same skill, harder or easier

We would put this in front of a grade 8 class. That is our judgement, not a standard, and it is printed here so you can disagree with it. Everything else we put in that year.