RHS: a right angle, the hypotenuse, a leg
A right angle is given. Can a compass arc still cross the other arm twice?
The rule
No: with a right angle, a compass arc crosses once at most.
In a right-angled triangle, the longest side is the hypotenuse. It sits opposite the right angle.
RHS means right angle, hypotenuse, and one leg. A leg is a side next to the right angle. Two right triangles with equal RHS parts are congruent.
Why? The two leg squares add to the hypotenuse square. So square the hypotenuse and take away the leg squared. Then take the square root. That gives the third side. Equal numbers give an equal third side. So all three sides match (SSS).
| Hypotenuse | Given leg | Third side |
|---|---|---|
| 13 | 5 | 12 |
| 10 | 6 | 8 |
| 25 | 7 | 24 |
Check the first row: 169 − 25 = 144, and 12² = 144.
Each pair has a right angle, a hypotenuse and a leg. Same triangle?
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