GCSE MATHSSession 22 – Vectors, Pythagoras Theorem,

Congruence and Similarity.

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.

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)

Vectors A vector is a way of showing translations if this shape has moved 4 right and 3 down. It has been translated by a vector of

The top number is horizontal movement (left is negative, right is positive)

The bottom number is vertical movement (down is negative, up is positive)

Ex27.3

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?

Vector addition

Vector PQ Vector QR Vector PR Vector RP

NegativesP

Q

R

What vector addition would we need to do to write the vector

PR

RP

Accurate construction of triangles

http://www.bbc.co.uk/schools/gcsebitesize/maths/geometry/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.

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

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

Problems involving PythagorasIncluding 3D problems Work through examples as a group p294 and p296

Examples of exam questions are available on page 298.

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.

Congruence

Similarity

Read through a few examples from chapter 32.

Try a few questions from Ex 32.1

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.