Diagram, givens, target
Mark every given on the diagram and state the target clearly. Start from a relationship that connects exactly those quantities.
German Gymnasium Klasse 7 / Mathematics / Curriculum
Geometrie: structured theory, worked examples, answered practice, and a mastery checklist for German Gymnasium Klasse 7.
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
Keep each unit in GR/DE: concept, German term, example, exercise, recap.
The structure follows the official textbook layout and is used to organise study.
Hypotenuse 25 cm, area 150 cm².
Before calculating, explain the key idea from “Winkelarten” and which conditions must be checked.
The answer should show not only which rule is used for “Winkelarten”, but also why it is valid here.
Geometrie
Try independently, use the hint if needed, then open the answer guide.
1. Explain the idea and give one correct foundation example for “Winkelarten”.
Write the givens, a useful representation or rule, and only then calculate.
A complete answer defines “Winkelarten”, shows equivalent steps, and includes a final check.
2. Solve an application and show every intermediate step for “Winkelsätze”.
Write the givens, a useful representation or rule, and only then calculate.
A complete answer defines “Winkelsätze”, shows equivalent steps, and includes a final check.
3. Compare a correct and an incorrect approach and justify the difference for “Dreieckskonstruktionen”.
Write the givens, a useful representation or rule, and only then calculate.
A complete answer defines “Dreieckskonstruktionen”, shows equivalent steps, and includes a final check.
4. Create a short exam-style question and check your answer for “Kongruenz in einfacher Form”.
Write the givens, a useful representation or rule, and only then calculate.
A complete answer defines “Kongruenz in einfacher Form”, shows equivalent steps, and includes a final check.
The areas that usually create mistakes or need extra revision.
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.