2TH §3.4 Calculating using similarity (discussing test Ch1)

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

§ 3.4 Calculating using similarity

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Exercises 18, 19, S20, S21

Calculating unknown sides in similar figures

When calculating unknown sides in similar figures, you can use the scale factor (see LessonUp §3.2).

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

• Do §3.4: S25, 27, S28, 28, 29

• Correct your answers with the Solutionsbook and a red pen
  

Discussing the test Chapter 1

Bowling. (2+2+2 points)

Jules goes bowling in the bowling center.

To rent a bowling alley (bowlingbaan) for the afternoon, he will have to pay € 27,50.  On top of that Jules will have to pay for drinks. Soft drinks cost € 1,50 per glass.

1    Explain why there is a linear relation between the number of drinks and the total

      amount of euro’s Jules has to pay? 

      There is a linear relation because for each glass of soda Jules pays € 1,50 (each time 

      the same amount)

2    Write down a formula to calculate the costs C in euro's for buying a soft drinks. 

      C = 1,50a + 27,5

3*  Jules got € 40 from his parents to spend at the bowling center.

        What is the maximum number of glasses of soft drinks he can buy?  C = 1,50a + 27,5 = 40

        1,50a = 12,5                        a = 12,5 : 1,50 = 8,33….                          He can buy 8 glasses of soft drink

Graph 1: gradient is ‒6 : 2 = ‒3, so y = ‒3x + 12

Graph 2: x = 2

Graph 3: gradient = 40 : 10 = 4, so y = 4x

Graph 4: y = ‒20

Table A: gradient is -8 : 1 = -8  ->  linear relation -> Formula w = -8t +21

Table B: gradient is 11 : 1 = 11 -> linear relation -> Formula w = 11t - 3

Table C: gradient is n.a. -> no linear relation, because not the same steps

Table D: gradient is 7 :1 = 7 -> linear relation -> Formula w = 7t

Formula A:       gradient is 2,    y- intercept is -8  -> Rising because gradient is positive

Formula B:       gradient is 0,    y- intercept is -4  -> Horizontal line

Formula C :      gradient is -2,   y- intercept is 8    -> Falling because gradient is negative

The first coordinate (x) goes up with 3 (7 ‒ 4 = 3).

The second coordinate (y) goes up with 6 (23 ‒ 17 = 6).

The gradient is 6 : 3 = 2. (vertical steps (y) divided by the horizontal steps (x))

y = 2x + b  -> fill in one of the points to calculate b.

17 = 2 × 4 + b

17 = 8 + b

b = 17 ‒ 8 = 9

y = 2x + 9

Total points 27 (blue card 25 points)

What did you learn today?