Diagram, givens, target
Mark every given on the diagram and state the target clearly. Start from a relationship that connects exactly those quantities.
Greek Gymnasium Grade 3 / Mathematics / Μέρος Β: Γεωμετρία - Τριγωνομετρία
Γεωμετρία: structured theory, worked examples, answered practice, and a mastery checklist for Greek Gymnasium Grade 3.
Unit
The essential chapter ideas in a clear sequence before practice.
Mark every given on the diagram and state the target clearly. Start from a relationship that connects exactly those quantities.
Every geometric step needs a property, theorem, or definition. A result without justification is not a complete proof.
Length, area, volume, and angle use different units. Round only at the end and keep sufficient intermediate precision.
Mathematics
Follow the method step by step and check why every step is valid.
A right triangle has perpendicular sides 15 cm and 20 cm. Find its hypotenuse and area.
Mathematics
A bridge year into Lyceum: students need confidence in algebraic manipulation and basic proof thinking.
The structure follows the official textbook layout and is used to organise study.
The areas that usually create mistakes or need extra revision.
Hypotenuse 25 cm, area 150 cm².
Before calculating, explain the key idea from “Ισότητα σχημάτων” and which conditions must be checked.
The answer should show not only which rule is used for “Ισότητα σχημάτων”, but also why it is valid here.
Γεωμετρία
Try independently, use the hint if needed, then open the answer guide.
1. Explain the idea and give one correct foundation example for “Ισότητα σχημάτων”.
Write the givens, a useful representation or rule, and only then calculate.
A complete answer defines “Ισότητα σχημάτων”, shows equivalent steps, and includes a final check.
2. Solve an application and show every intermediate step for “Ομοιότητα σχημάτων”.
Write the givens, a useful representation or rule, and only then calculate.
A complete answer defines “Ομοιότητα σχημάτων”, shows equivalent steps, and includes a final check.
3. Compare a correct and an incorrect approach and justify the difference for “Θεώρημα Θαλή”.
Write the givens, a useful representation or rule, and only then calculate.
A complete answer defines “Θεώρημα Θαλή”, shows equivalent steps, and includes a final check.
4. Create a short exam-style question and check your answer for “Όμοια τρίγωνα”.
Write the givens, a useful representation or rule, and only then calculate.
A complete answer defines “Όμοια τρίγωνα”, shows equivalent steps, and includes a final check.
Where to start: textbook, daily material, PDFs, videos, and worked examples.
Targeted practice before full tests so coverage is clear.
How to measure progress in this chapter and when it enters a cumulative mock.
What to do after finishing the chapter and how it connects to the next unit.
Note: for the official examinable syllabus of each school year, always confirm with the school, tutor, and current Ministry/IEP announcements.