Properties And Constructions
Overview
Geometry is the part of this course where a correct answer is not enough. A specimen paper asks for the size of an angle and then adds three words, give a reason, and the mark scheme insists on the words centre and circumference appearing in the answer. Another asks you to show that an angle is 30 degrees, where the value is printed in the question and every mark is for the chain of reasoning that gets there.
This topic, references G1 to G13, is that chain of reasoning and the vocabulary it is written in. You will use the conventional terms and notation, work with angles at a point and on a straight line, use the angle properties of parallel and intersecting lines, triangles and quadrilaterals, calculate interior and exterior angles of polygons, recognise reflection and rotation symmetry, understand congruence and similarity, name the parts of a circle, describe three dimensional solids and their plans and elevations, read bearings and scale drawings, and carry out the standard ruler and compass constructions and loci problems. On the Extension Tier you add the conditions for congruent triangles, the standard circle theorems and their use in proof, and the construction of plans and elevations.
Objectives
- [Core] use conventional terms and notations: points, lines, vertices, edges, planes, parallel lines, perpendicular lines, right angles, polygons and regular polygons
- [Core] use the standard conventions for labelling and referring to the sides and angles of triangles
- [Core] recall and use properties of angles at a point, angles at a point on a straight line including right angles and perpendicular lines; vertically opposite angles
- [Core] understand and use the angle properties of parallel and intersecting lines, triangles and quadrilaterals (Notes: students should know the meaning and properties of ‘alternate’, ‘corresponding’ and ‘interior’ angles. Colloquial terms such as ‘Z angles’ should not be used. Students should know the names and properties of isosceles, equilateral and scalene triangles, and also right-angled, acute-angled and obtuse-angled triangles)
- [Core] calculate and use the sums of the interior and exterior angles of polygons (Notes: students should be able to calculate the values of the interior angle, exterior angle and angle at the centre of regular polygons)
- [Core] recall the properties and definitions of special types of quadrilateral, including square, rectangle, parallelogram, trapezium, kite and rhombus
- [Core] recognise reflection and rotation symmetry of 2D shapes
- [Core] understand congruence and similarity
- [Core] calculate lengths of similar figures
- [Extension] understand and use conditions for congruent triangles
- [Core] identify and apply circle definitions and properties, including: centre, radius, chord, diameter, circumference including: tangent, arc, sector and segment
- [Extension] apply the standard circle theorems concerning angles, radii, tangents and chords, and use them to prove related results (Notes: including angle subtended by an arc at the centre is equal to twice the angle subtended at any point on the circumference, angle subtended at the circumference by a semicircle is 90°, angles in the same segment are equal, opposite angles in a cyclic quadrilateral sum to 180°, tangent at any point on a circle is perpendicular to the radius at that point, tangents from an external point are equal in length, the perpendicular from the centre to a chord bisects the chord, alternate segment theorem)
- [Extension] geometrical reasoning and proof: use standard theorems to justify results in geometric contexts
- [Core] identify properties of the faces, surfaces, edges and vertices of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres
- [Core] interpret plans and elevations of 3D shapes
- [Extension] construct and interpret plans and elevations of 3D shapes
- [Core] measure line segments and angles in geometric figures, including interpreting maps and scale drawings and use of scale factors and bearings (Notes: including the eight compass point bearings and three-figure bearings)
- [Core] use the standard ruler and compass constructions (perpendicular bisector of a line segment, constructing a perpendicular to a given line from/at a given point, bisecting a given angle, constructing an angle of 60°)
- [Core] use these to construct given figures and solve loci problems
- [Core] know that the perpendicular distance from a point to a line is the shortest distance to the line
Mind map
This topic is mapped out so you can see how the ideas connect.
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Lesson Note
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Lesson Evaluation
Congratulations on completing the lesson on Properties And Constructions. 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.
- The bearing of B from A is 072 degrees. What is the bearing of A from B? A. 108 degrees B. 172 degrees C. 252 degrees D. 288 degrees Answer: C
- A regular polygon has an exterior angle of 24 degrees. How many sides does it have? A. 12 B. 15 C. 20 D. 24 Answer: B
- Which condition does NOT prove that two triangles are congruent? A. SSS B. SAS C. AAA D. RHS Answer: C
- A and B are points on a circle with centre O, and C is a third point on the circumference. Angle ACB is 40 degrees. What is angle AOB? A. 20 degrees B. 40 degrees C. 80 degrees D. 140 degrees Answer: C
- Which quadrilateral has diagonals that bisect each other at right angles but does not have four equal angles? A. Square B. Rectangle C. Rhombus D. Trapezium Answer: C
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Work through these questions in the app
Recommended Books
Practice Mock Questions
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