GANITA PRAKASH · GRADE 7 · PART II · CHAPTER 1
MATCH — Same shape. Same size.
Think first. Use AI purposefully. Verify always.
DISCOVER
Start with a sketch and a prediction.
Turn a paper triangle over. Has it become a different size? What would count as evidence that two figures are exact copies?
Try on paper first. Use the model to test your idea before accepting the explanation.
Understand
Congruent figures fit exactly after a translation, rotation or reflection. Every part must match. Equal area alone does not establish congruence; a change of scale generally destroys it.
Key Ideas
Same shape + same size → congruence
Orientation does not affect congruence. Same shape with different size is not enough.
Visualise
Move without stretching
Solid and dashed copies have the same side lengths. Predict how to align them.
Method
Choose a pair of corresponding points. Move, turn or flip one figure without stretching it. Check the entire boundary, not just one side.
Worked Example
Given
Two circles of radius 3 cm.
To Find
Whether the circles are congruent
Property
A circle is fixed by its radius.
Solution
- Move one centre onto the other.
- Both boundaries are exactly 3 cm from that centre.
Result
The circles are congruent.
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
A 2 cm by 6 cm rectangle and a 3 cm by 4 cm rectangle each have area 12 . Must they be congruent?
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 2