2Tvwo § 4.4 Calculating using similarity

• Wiskunde
• Middelbare school
• havo, vwo
• Leerjaar 2

§ 4.4 Calculating using similarity

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Calculating unknown sides in similar figures

When calculating unknown sides in similar figures, you can use the scale factor (see LessonUp §4.2).

To make it easier to find out which sides are corresponding sides, you should sketch both figures in the same position.

Watch the following example!

Example

Triangle ABC and triangle PQR are similar figures. Calculate the length of AC and PR.

Sketch

Here a better sketch 

is added.

Now the triangles 

are in the same position.

Calculations

Before we go on ...

here comes a non-math slide !

Scale factor and perimeter

Perimeter rectangle A = 2 + 1 + 2 + 1 = 6 cm

Perimeter rectangle B = 4 + 2 + 4 + 2 = 12 cm

Perimeter rectangle C = 6 + 3 + 6 + 3 = 18 cm

Perimeter rectangle D = 8 + 4 + 8 + 4 = 24 cm

12 = 6 x 2; 18 = 6 x 3; 24 = 6 x 4.

The perimeter is multiplied by the scale factor.

Scale factor and area (1)

Rectangles B, C and D are

enlargements of rectangle A.

The scale factors are:

B: 2 (meaning: when you 

multiply length and width of picture

A by 2, you get picture B)

C: 3

D: 4

Scale factor and area (2)

The area is multiplied by the scale factor squared!

Scale factor and area

When the dimensions (length/width/height) of a figure are multiplied by a factor s, the perimeter is also multiplied by s, but the area is multiplied by      .

(When you learn about volume you will find that the volume is multiplied by      )

s​2​​

s​3​​

Homework

• Make §4.4:

Support: 24, 25, S26, 27, S28, 28, 29

Standard: 24, 25, 26, 27, 28, 29, 30

Challenge: 24, 26, 27, 28, 29, 30, C5

• Correct your answers with the Solutionsbook and a red pen
  

What did you learn today?