Geometrical Properties And Reasoning
Overview
A tiled floor, a bridge truss and a kite in flight are all held together by the same handful of angle facts. This topic gives you the standard geometric statements Edexcel expects you to quote, and the discipline of chaining them together so that every angle you state is backed by a named reason rather than a guess.
You will work through parallel line angle pairs, polygon angle sums for any number of sides, the defining properties of each quadrilateral in the special-quadrilateral family, and the three kinds of symmetry a 2D shape can carry. By the end you should be able to look at an unfamiliar diagram, identify which properties apply, and write a clean chain of reasoning from what is given to what is asked.
Objectives
- Understand and apply geometrical properties of Euclidean space
- Use geometrical reasoning to solve problems
- Understand and use angle properties of parallel lines, triangles and polygons, including regular polygons
- Know and use properties of the parallelogram, rectangle, square, rhombus, trapezium and kite
- Understand and use symmetry about a point, line or plane, including recognising line and rotational symmetry
Mind map
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Flashcards
Quick recall practice on the facts this topic is tested on.
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Lesson Note
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Lesson Evaluation
Congratulations on completing the lesson on Geometrical Properties And Reasoning. Now that youve explored the key concepts and ideas, its time to put your knowledge to the test. This section offers a variety of practice questions designed to reinforce your understanding and help you gauge your grasp of the material.
You will encounter a mix of question types, including multiple-choice questions, short answer questions, and essay questions. Each question is thoughtfully crafted to assess different aspects of your knowledge and critical thinking skills.
Use this evaluation section as an opportunity to reinforce your understanding of the topic and to identify any areas where you may need additional study. Don't be discouraged by any challenges you encounter; instead, view them as opportunities for growth and improvement.
- Two parallel lines are crossed by a transversal. One angle is 73 degrees and its alternate angle is on the opposite side of the transversal, between the parallel lines. What is the size of the alternate angle? A) 17 degrees B) 73 degrees C) 107 degrees D) 180 degrees Answer: B
- A regular polygon has an exterior angle of 24 degrees. How many sides does it have? A) 12 B) 15 C) 18 D) 24 Answer: B
- Which quadrilateral has diagonals that bisect each other at 90 degrees but are NOT necessarily equal in length? A) Rectangle B) Rhombus C) Trapezium D) Kite Answer: B
- A shape has rotational symmetry of order 2 but no lines of symmetry. Which shape is this most likely to be? A) Square B) Isosceles trapezium C) Parallelogram that is not a rectangle or rhombus D) Regular hexagon Answer: C
- The interior angle sum of a polygon is 1440 degrees. How many sides does the polygon have? A) 8 B) 9 C) 10 D) 12 Answer: C
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Practice Mock Questions
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