RHS: a right angle, the hypotenuse, a side
Two triangles share some parts. Must they be twins?
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- A leg FG of 6 cm. A leg is a side next to the right angle.
- A line through F, square to FG. Square here means at 90°.
- An arc of 10 cm from G cuts the line twice.
- The two triangles are mirror twins.
The rule
Not always. Two triangles with some equal parts may still differ.
RHS stands for right angle, hypotenuse, side. Take two right-angled triangles. Suppose their hypotenuses are equal. Suppose one more side is equal. Then they are congruent. The hypotenuse is the side across from the right angle.
The arc cuts the square line above and below. The two triangles are mirror images. So they are congruent.
Take two sides and an angle that is not between them. They do not always fix a triangle. Try sides of 5 and 6 cm. Put a 40° angle across from the 5 cm side. Two triangles fit. With a right angle, the hypotenuse and one leg do settle it. They fix one triangle. The hypotenuse alone does not.