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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.
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Theorem and Converse
What is it?
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.
In simple words
- 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
Important terms
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.
What you should learn
- 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.
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
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.
EXAM APPLICATION
State the correct term, connect it to the chapter rule or evidence, and use a clear example or calculation.
Recommended for Class 10
Full school-level explanation
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.
Learn the idea, then use it:
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.
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.
Remember
- 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
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.
Remember
- correct term
- chapter link
- clear application
Examples
- Define first
- Show the rule or evidence
- Check units, labels, and conclusion
Remember
- 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
- keep the ideas separate
- 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
- correct term
Deeper understanding
Go beyond memorising Theorem and Converse. Connect the definition to reasons, relationships, exceptions, and exam wording.
Common mistakes
Exam focus
Core Idea
Key Points
Simple Check
How to Answer
Exam focus
Quick revision
- 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
- keep the ideas separate
- Theorem And Converse: If AB=CD then distance from O to AB equals distance from O to CD. If the distances match, the chords
- 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
Do not merge theorem and converse with a neighbouring idea that uses a different definition, rule, or method.
For long answers on Theorem and Converse: define clearly → explain the main parts → give one example → state one exam caution.
Exam Focus
Exam Focus
Important 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
- keep the ideas separate
Important formulas
- distance from O
- equal chords <=> equal distance
- keep the ideas separate
Common exam traps
- Do not merge theorem and converse with a neighbouring idea that uses a different definition, rule, or method.
- Do not invent a formula, fact, unit, or diagram label that the chapter does not support.
Long question structure
Definition → key parts → example → exam caution
Common Mistakes
Common Mistakes
- Mistake
Do not merge theorem and converse with a neighbouring idea that uses a different definition, rule, or method.
- Mistake
Do not invent a formula, fact, unit, or diagram label that the chapter does not support.
- Mistake
Do not merge theorem and converse with a neighbouring idea that uses a different definition, rule, or method.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
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
keep the ideas separate
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 alw
equal chords <=> equal distance
- 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 alw
- Formula
- equal chords <=> equal distance
- Example
- distance from O
- Critical warning
- Do not merge theorem and converse with a neighbouring idea that uses a different definition, rule, or method.
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Exam Practice
Define
Q1. Define Theorem and Converse.
Explain
Q2. Explain: CORE UNDERSTANDING.
Example
Q3. Give one clear example of Theorem and Converse and say why it fits.
Mistake
Q4. State one common mistake students make about Theorem and Converse.
Exam note
Q5. Write a short exam note on Theorem and Converse: definition, two points, one example.
Sources & References
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.