MathematicsChapter 10: Practical Geometry
Impossible Angle Pairs
If two given angles already sum to 180 deg or more, the triangle is impossible.
Learning objectives
- Define and explain impossible angle pairs.
- Apply impossible angle pairs to a focused FBISE question.
- Check the answer for correct terms, evidence, working, and units.
Definition
If two given angles already sum to 180 deg or more, the triangle is impossible. A triangle cannot hold 190 deg in two corners. Check the sum before you start construction. If the sum is less than 180 deg, compute the third angle and then draw: copy one angle at an end of the given side, copy the other angle at the other end (ASA), and let the arms meet.
Where / symbols
- Impossible Angle Pairs
- If two given angles already sum to 180 deg or more, the triangle is impossible. A triangle cannot hold 190 deg in two corners. Check the sum before you start construction. If the sum is less than 180 deg, compute the third angle and then draw: copy one angle at an end of the given side, copy the other angle at the other end (ASA), and let the arms meet.
Overview
Learn the idea, then use it:
Core Understanding
If two given angles already sum to 180 deg or more, the triangle is impossible. A triangle cannot hold 190 deg in two corners. Check the sum before you start construction. If the sum is less than 180 deg, compute the third angle and then draw: copy one angle at an end of the given side, copy the other angle at the other end (ASA), and let the arms meet.
Examples 190 · impossible · two angles · IMPOSSIBLE ANGLE PAIRS: If two given angles already sum to 180 deg or more, the triangle is impossible. A triangle cannot hold 190 deg in two co
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 — IMPOSSIBLE ANGLE PAIRS
If two given angles already sum to 180 deg or more, the triangle is impossible. A triangle cannot hold 190 deg in two corners. Check the sum before you start construction. If the sum is less than 180 deg, compute the third angle and then draw: copy one angle at an end of the given side, copy the other angle at the other end (ASA), and let the arms meet.
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 impossible angle pairs with a neighbouring idea that uses a different definition, rule, or method.
Key points
- 190
- impossible
- two angles
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Impossible Angle Pairs
Sticky Notes · Quick Revision
Core Idea
- If two given angles already sum to 180 deg or more, the triangle is impossible.
Key Points
- 190
- impossible
- two angles
Simple Check
- Explain impossible angle pairs 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 impossible angle pairs 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 two given angles already sum to 180 deg or more, the triangle is impossible.
- 190
- impossible
- two angles
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