term 3 topic test

Seite 1

Similar Figures revision

The Tranfiguration Transformation

side OA times 3 gives 9 spaces, corresponding ray gives enlarged shape

c) * points are between PR are seen passing through

ii) PS PS', PR PR', PQ PQ'

Seite 2

2 figures are similar if one is an enlargement (or reduction)

example explain:

PQR and ABC ar similar figures, triangle PQR has been enlarged from PQR ,

a) find the centre of enlargement

factor of enlargement = new shape

_____________

old shape

a) rays from points (AP, CR, BQ) , point of intersection is the centre of enlargement (W)

b) k = 7.5 distance of WR /

5 units of WC

draw a concluding line towards one meeting point

Seite 3

Investigation 2 -

*1 the matching angles are equal and 2 ) the matching sides are in the same ratio. ( sides are therefore in proportion)

*the ratio of the lengths of the sides shows the enlargement factor.

- figures are similar due to their properties ,angles ae equal and corresponding sides are in the same ratio

enlargement factor is found by drawing 9/6 , so hence to find x , 9/6 times 7 ..enlargement factor to enlarge or reduct one side..

Seite 4

testing triangles for similarity

in triangle ABC and CDE :

/BAC = /CDE ( alternating angles on // lines)

/ABC =/CDE (alt,angles )

/ACB = /DCE (VERT. OPP)

THEREFORE, ABC & CDE (AAA)

Seite 5

Making a scale drawing

Find the real lengths involved

decide how large the drawing will be

choose a appropriate scale

transfer te real lengths into scale lengths using the scale

*to decide on a scale, find the ratio of thelength available for the drawing to the length of the real object.

scale = length of drawing:length of object

Example 1- a scale drawing 7.5*5.5