Altitude to hypotenuse relations
In a right triangle, the altitude from the right angle to the hypotenuse creates two smaller triangles that are similar to the original triangle and to each other.
Practice This ConceptMain explanation
Teacher explanation
Because those triangles are similar, the altitude and the split hypotenuse segments follow special square-type relations. This is one of the most useful results in right-triangle geometry.
Example
If the hypotenuse is split into 4 cm and 9 cm, then the altitude is 6 cm because h² = 4 × 9.
Simple analogy
Altitude is the geometric mean of the split hypotenuse parts.
Common confusion
Students often add the two hypotenuse segments or use the wrong side relation.
Exam tip
Label the two parts of the hypotenuse before using h² = pq.
Answer writing and exam use
1-mark use
Write the exact meaning of altitude to hypotenuse relations in one clean line.
2-mark use
Define altitude to hypotenuse relations and add one example or condition.
3-mark use
Explain altitude to hypotenuse relations, show the method or example, and mention the common mistake.
Practice this concept with focused MCQs
Open the concept quiz intro first, review the test details, and then start a focused MCQ set from this concept only. Instant score and answer review are live now.
Help improve this page
Found something confusing, incorrect, or missing?