Geometry

Classification of Solids

Faces, Edges and Vertices in Polyhedra

Measuring, Estimating and Drawing Angles

Angles at a Point & vertically Opposite Angles

Types of Triangles

Types of Quadrilaterals

Lengths in Polygons on the Plane

Visualising Solids

Cross Sections of Solids

Lines, Segments and Rays

Complementary and Supplementary Angles

Angles in Triangles

Interior and Exterior Angles of Polygons

Exterior Angle Sum and other Calculations

Cointerior Angles

Alternate Angles

Corresponding Angles

Angles and Parallel Lines

Identifying Parallel Lines

Constructions with a compass

Angles in Quadrilaterals

Lengths in Quadrilaterals

Properties of Quadrilaterals

Identifying Polygons from angle conditions

Drawing and Recognising Shapes with Properties (Investigation)

Triangle problems

Angles in Triangles Revision

Angles and Lengths in Quadrilaterals Revision

Shapes in Fractal Geometry

Symmetries in 3-D Shapes

Angles on Parallel Lines Revision

Harder Angles on Parallel Lines

Centres of Triangles

Geometrical Calculations

Deductive Proofs

Proofs with Triangles

Proofs with Quadrilaterals

Stage 1 - Stage 3

Proofs with Quadrilaterals

Lesson

We've just started our journey on constructing geometrical proofs using deductive reasoning.

We can use proofs to show that various angles have particular values or equivalences or as we will practice in this lesson, use proofs to verify relationships within quadrilaterals.

Examples

Question 1

Prove that $x$x and $y$y are complementary angles.

Question 2

Let $s$s be the sum of exterior angles in quadrilateral $BCEG$BCEG. By using the fact that the angle sum of a quadrilateral is $360^\circ$360°, show that $s=360$s=360

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