🔺 Congruence Criteria for Right Triangles
Big Idea: Right triangles are special because we always know one angle — the right angle (90°). This means we need fewer pieces of information to prove two right triangles are congruent compared to general triangles.
⭐ Why Are Right Triangles Special?
Recall the general triangle congruence criteria: SAS ASA AAS SSS
Each of these requires 3 pieces of information. But in a right triangle, one piece is already given for free — the 90° angle!
Key Insight: Since both right triangles already share a right angle, we only need 2 additional matching parts instead of 3. This gives us 4 special criteria for right triangles.
Terminology Reminder:
- Legs — the two sides that form the right angle
- Hypotenuse — the side opposite the right angle (the longest side)
- Acute angles — the two angles that are less than 90°
Parts of a Right Triangle
Interactive visualization — available in the full lesson