Triangles — Concept Maps
Jammu & Kashmir Board · Class 10 · Mathematics
4 concept maps of Triangles for Jammu & Kashmir Board Class 10 Mathematics, each also written out as a text outline.
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Decision Tree: Which Similarity Criterion to Use?
The map in words
- Two Triangles Given
- B
- 3 angles known: C
- Yes - 2 angles equal: F
- N
- Yes - 3 angles equal: G
- No: H
- Yes - 2 angles equal: F
- Sides known: D
- Yes - all 3 equal: I
- Only 2 equal: J
- No: Not similar
- Mixed info: E
- Yes - INCLUDED angle: L
- Angle NOT included: M
- 3 angles known: C
- B
- is
- corresponding
- angles
- ratios
- AND
- it
- Triangles
- by
- or
- Check
- with
Chapter 6 Triangles - Key Concepts Overview
The map in words
- Triangles
- Similar Figures
- Same shape
- Not same size
- All circles similar
- All squares similar
- BPT Thales Theorem
- DE parallel BC
- AD over DB equals AE over EC
- Converse also true
- Similarity Criteria
- AA Criterion
- Two angles equal
- AAA Criterion
- Three angles equal
- SSS Criterion
- All sides proportional
- SAS Criterion
- Two sides proportional
- Included angle equal
- AA Criterion
- Area Theorem
- Ratio of areas
- Square of side ratio
- Key Notation
- Tilde for similar
- Congruent vs Similar
- Similar Figures
Chapter 6 Triangles — Complete Concept Map
The map in words
- Triangles Ch 6
- Similar Figures
- Same shape different size
- All circles similar
- All squares similar
- All equilateral triangles similar
- Congruent implies Similar
- Similar does NOT imply Congruent
- Polygon Similarity
- Condition 1 Equal Angles
- Condition 2 Proportional Sides
- Both conditions needed for polygons
- One condition enough for triangles
- BPT Thales Theorem
- DE parallel BC
- AD over DB equals AE over EC
- Proof uses Area Method
- Converse also true
- Similarity Criteria
- AAA Three angles equal
- AA Two angles equal
- SSS Sides proportional
- SAS Sides proportional and included angle equal
- RHS Right triangles only
- Applications
- Indirect Measurement
- Heights of Mountains
- Distance of Moon
- Scale Factor in Maps
- Similar Figures
Triangles and Similarity
The map in words
- Triangles and Similarity
- Similar Figures
- Similarity of Polygons
- Similarity of Triangles
- Basic Proportionality Theorem
- Converse of BPT
- Triangle Similarity Criteria
- AAA / AA Criterion
- SSS Criterion
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