MathematicsChapter 9: Chord and Arcs of a Circle
Theorem and Converse
If AB=CD then distance from O to AB equals distance from O to CD.
Learning objectives
- Define and explain theorem and converse.
- Apply theorem and converse to a focused FBISE question.
- Check the answer for correct terms, evidence, working, and units.
Definition
If AB=CD then distance from O to AB equals distance from O to CD. If the distances match, the chords match. Do not claim equal chords are always parallel or always diameters.
Formula
AB=CD then distance from O to AB equals dis
Where / symbols
- Theorem And Converse
- If AB=CD then distance from O to AB equals distance from O to CD. If the distances match, the chords match. Do not claim equal chords are always parallel or always diameters.
Relationship
- equal chords <=> equal distance
Overview
Learn the idea, then use it:
Core Understanding
If AB=CD then distance from O to AB equals distance from O to CD. If the distances match, the chords match. Do not claim equal chords are always parallel or always diameters.
Examples distance from O · equal chords <=> equal distance · THEOREM AND CONVERSE: If AB=CD then distance from O to AB equals distance from O to CD. If the distances match, the chords match. Do not claim · Exam tip: Equal distance means the perpendicular distances, not the lengths along a radius to an endpoint (tho
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 — THEOREM AND CONVERSE
If AB=CD then distance from O to AB equals distance from O to CD. If the distances match, the chords match. Do not claim equal chords are always parallel or always diameters.
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 theorem and converse with a neighbouring idea that uses a different definition, rule, or method.
Key points
- distance from O
- equal chords <=> equal distance
- THEOREM AND CONVERSE: If AB=CD then distance from O to AB equals distance from O to CD. If the distances match, the chords match. Do not claim
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Theorem and Converse
Sticky Notes · Quick Revision
Core Idea
- If AB=CD then distance from O to AB equals distance from O to CD.
Key Points
- distance from O
- equal chords <=> equal distance
- THEOREM AND CONVERSE: If AB=CD then distance from O to AB equals distance from O to CD. If the distances match, the chords match. Do not claim
Simple Check
- Explain theorem and converse 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 theorem and converse 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
- If AB=CD then distance from O to AB equals distance from O to CD.
- distance from O
- equal chords <=> equal distance
- THEOREM AND CONVERSE: If AB=CD then distance from O to AB equals distance from O to CD. If the distances match, the chords match. Do not claim
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