GANITA PRAKASH · GRADE 7 · PART II · CHAPTER 1
ORDER — Correspondence carries meaning
Think first. Use AI purposefully. Verify always.
DISCOVER
Start with a sketch and a prediction.
If AB matches XY and AC matches XZ, which vertex must A match? Explain using the shared endpoints.
Try on paper first. Use the model to test your idea before accepting the explanation.
Understand
The order in a congruence statement records a vertex-by-vertex match. For △ABC ≅ △XYZ, A ↔ X, B ↔ Y, C ↔ Z. Corresponding sides and angles follow that same mapping.
Key Ideas
Naming the same two triangles with an arbitrary order can state a false correspondence.
Visualise
Match vertices before writing the order
Correct order: A ↔ X, B ↔ Y, C ↔ Z.
Method
List the equal side pairs. Match the shared endpoints. Write the second triangle in the same order as the first, then check every side and angle.
Worked Example
Given
△HEN ≅ △BIG.
To Find
Equivalent ordered statements for the same correspondence
Property
H ↔ B, E ↔ I, N ↔ G must remain paired.
Solution
- Permute both lists in the same way.
- HNE ↔ BGI; EHN ↔ IBG; ENH ↔ IGB; NHE ↔ GBI; NEH ↔ GIB.
Result
The five other orders preserve the original vertex mapping.
AIMS Method
- A — Attempt independently
Sketch and predict before using a criterion. - I — Investigate the idea
Separate given facts from visual assumptions. - M — Make connections
Match vertices, sides and angles consistently. - S — Scrutinise your reasoning
Check each hypothesis and justify the conclusion.
Think first. Use AI purposefully. Verify always.
Focused Practice
In △AIR ≅ △FLY, which side corresponds to IR and which angle to ∠R?
Check & Feedback
Name the exact given facts, state a valid criterion or explain why none applies, and check the vertex order.
Textbook connection: Ganita Prakash · Grade 7 · Part II · Chapter 1 — Geometric Twins · printed page 7