MathematicsChapter 10: Practical Geometry
Altitudes and Orthocentre
The three altitudes meet at the orthocentre.
Learning objectives
- Define and explain altitudes and orthocentre.
- Apply altitudes and orthocentre to a focused FBISE question.
- Check the answer for correct terms, evidence, working, and units.
Definition
The three altitudes meet at the orthocentre. In an acute triangle the orthocentre lies inside. In a right triangle it sits at the right-angle vertex (the two legs are already altitudes). In an obtuse triangle it lies outside, because two altitudes fall on extensions of the sides.
Where / symbols
- Altitudes And Orthocentre
- The three altitudes meet at the orthocentre. In an acute triangle the orthocentre lies inside. In a right triangle it sits at the right-angle vertex (the two legs are already altitudes). In an obtuse triangle it lies outside, because two altitudes fall on extensions of the sides.
Overview
Learn the idea, then use it:
Core Understanding
The three altitudes meet at the orthocentre. In an acute triangle the orthocentre lies inside. In a right triangle it sits at the right-angle vertex (the two legs are already altitudes). In an obtuse triangle it lies outside, because two altitudes fall on extensions of the sides.
Examples orthocentre · inside · right-angle vertex · ALTITUDES AND ORTHOCENTRE: The three altitudes meet at the orthocentre. In an acute triangle the orthocentre lies inside. In a right triangle it si
Exam Application
State the correct term, connect it to the chapter rule or evidence, and use a clear example or calculation.
Examples Define first · Show the rule or evidence · Check units, labels, and conclusion
WHAT — ALTITUDES AND ORTHOCENTRE
The three altitudes meet at the orthocentre. In an acute triangle the orthocentre lies inside. In a right triangle it sits at the right-angle vertex (the two legs are already altitudes). In an obtuse triangle it lies outside, because two altitudes fall on extensions of the sides.
HOW — Use the idea
Identify what is given, select this topic's rule or evidence, apply it one step at a time, and check the result.
In simple words
Do not merge altitudes and orthocentre with a neighbouring idea that uses a different definition, rule, or method.
Key points
- orthocentre
- inside
- right-angle vertex
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Altitudes and Orthocentre
Sticky Notes · Quick Revision
Core Idea
- The three altitudes meet at the orthocentre.
Key Points
- orthocentre
- inside
- right-angle vertex
Simple Check
- Explain altitudes and orthocentre in your own words and connect it to one chapter example.
How to Answer
- Define the idea, show the main rule or evidence, apply it, and check the final statement.
Common Mistake
- Do not merge altitudes and orthocentre with a neighbouring idea that uses a different definition, rule, or method.
FBISE Exam Tip
- Use the exact term, show working where needed, and include units or labelled evidence.
60-second revision
- The three altitudes meet at the orthocentre.
- orthocentre
- inside
- right-angle vertex
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