GANITA PRAKASH · GRADE 7 · PART II · CHAPTER 1
TRIPLE — Three sides determine a triangle
Think first. Use AI purposefully. Verify always.
DISCOVER
Start with a sketch and a prediction.
Two construction circles intersect above and below a base. Do the intersections create two different shapes or reflected copies?
Try on paper first. Use the model to test your idea before accepting the explanation.
Understand
SSS fixes a non-degenerate triangle up to a rigid movement or reflection. Three positive lengths must satisfy the triangle inequality; invalid lengths do not create a triangle.
Key Ideas
SSS — three corresponding sides
Two circle intersections do not by themselves mean two non-congruent triangles.
Visualise
Meet at the circle intersections
AB = 6 cm, AE = 4 cm, BE = 8 cm. △ABE ≅ △ABF by SSS.
Method
Draw AB = 6 cm. Use circles centred at A and B with radii 4 cm and 8 cm. Join either intersection to A and B. Compare both constructions by reflection in AB.
Worked Example
Given
AB = 6 cm; AE = AF = 4 cm; BE = BF = 8 cm.
To Prove
△ABE ≅ △ABF
Property
SSS; the construction circles fix the three side pairs.
Proof
- AB = AB is common.
- AE = AF and BE = BF are radii of the respective construction circles.
- Match A ↔ A, B ↔ B, E ↔ F.
Result
△ABE ≅ △ABF; reflection in AB superimposes them.
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
Can side lengths 2 cm, 3 cm and 5 cm form a non-degenerate triangle?
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 5