1. Session 22 – Vectors, Pythagoras Theorem, Congruence and Similarity.

2. Homework  Complete some of the measures and constructions section on BKSB, Specifically LOCI constructions, since we did not cover this in class.  Also look at ‘congruence’ in the properties of angles and shapes section, and look at chapter 32 in the book.

3. Vectors  You should have completed vectors on BKSB. Vectors have a size (magnitude) and a direction.  10 minutes discuss this before moving on (next few slides) Show addition/subtraction of column vectors  Last week we represented vector quantities as column vectors in translations (see next slide)

4. Vectors

5.  Vectors can also be represented as a line, the length of the line represents the magnitude, and the slope of the line creates the direction (shown with an arrow  What would be the column vector for AB?  What would it be for BA?

6. Vector addition  Vector PQ  Vector QR  Vector PR  Vector RP

7. Negatives P Q R  What vector addition would we need to do to write the vector  PR  RP

8. Accurate construction of triangles  http://www.bbc.co.uk/schools/gcsebitesize/maths/g eometry/locirev4.shtml http://www.bbc.co.uk/schools/gcsebitesize/maths/g eometry/locirev4.shtml Construct a triangle with side lengths of 6cm, 5cm and 4cm. Solution  Use a ruler to draw a 6cm line. Label one end A and the other B.  Open the compass to a radius of 5cm.  Place the compass needle at point A and draw an arc above the line.  Open the compass to a radius of 4cm.  Move the compass needle to point B and draw an arc above it.  Join each end of the line to the point where the arcs cross.

9. Pythagoras’ Theorem  Used for right angled triangles only  The square on the hypotenuse is equal to the sum of the squares of the other two sides

11.  Example 292  Ex28.1 10 min  Rearranging formula to find one of the other sides  Ex28.2 10 min  Feel free to move onto more challenging questions in 28.3 and 28.5 when you feel ready

12. Problems involving Pythagoras Including 3D problems  Work through examples as a group  p294 and p296  Examples of exam questions are available on page 298.

13. Congruence and similarity  When two shapes are the same shape and size, like identical copies of each other, they are said to be congruent. (reflections, rotations and translations)  When one shape is an enlargement of another, they are said to be similar. The shapes are the same, the angles are the same and the lengths are in proportion (scale factor)  They may also be rotated or reflected but will be larger or smaller than the original.

14. Congruence Similarity

15.  Read through a few examples from chapter 32.  Try a few questions from Ex 32.1

16. Homework  Complete some of the measures and constructions section on BKSB, Specifically LOCI constructions, since we did not cover this in class.  Also look at ‘congruence’ in the properties of angles and shapes section, and look at chapter 32 in the book.