GANITA PRAKASH · GRADE 7 · PART II · CHAPTER 1
FIX — Which measurements fix a copy?
Think first. Use AI purposefully. Verify always.
DISCOVER
Start with a sketch and a prediction.
Two arms have lengths 4 cm and 8 cm. Can they open to different angles while keeping both lengths?
Try on paper first. Use the model to test your idea before accepting the explanation.
Understand
Measurements must fix both shape and size. A circle needs its radius. A rectangle needs its two adjacent side lengths. A two-arm symbol also needs the angle between its arms.
Key Ideas
Two arm lengths + included angle
Two given sides alone leave the hinge free to move.
Visualise
What is still free to move?
AB = 4 cm and BC = 8 cm throughout. The angle changes the shape. Set 80° to recover the source symbol.
Method
Ask what can still move when a measurement is fixed. Add enough information to remove that freedom. Do not confuse a flexible two-arm symbol with a rigid triangle.
Worked Example
Given
A two-arm symbol with AB = 4 cm, BC = 8 cm and ∠ABC = 80°.
To Find
Measurements needed for an exact copy
Property
The included angle is at the shared endpoint B.
Solution
- Draw BC of length 8 cm.
- At B construct an 80° ray and mark A at distance 4 cm.
- The opposite-side construction is a reflected copy.
Result
The arm lengths and included angle determine a congruent copy.
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
Would the perimeter alone determine a rectangle?
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 3