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

§ 3.4 Calculating using similarity
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§ 3.4 Calculating using similarity
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Slide 1 -Tekstslide

Questions about the homework?
Exercises 18, 19, S20, S21

Slide 2 -Tekstslide

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!

Slide 3 -Tekstslide

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

Slide 4 -Tekstslide

Sketch
Here a better sketch
is added.
Now the triangles
are in the same position.

Calculations

Slide 6 -Tekstslide

Before we go on ...
here comes a non-math slide !

Slide 8 -Tekstslide

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.

Slide 9 -Tekstslide

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

Slide 10 -Tekstslide

Scale factor and area (2)

The area is multiplied by the scale factor squared!

Slide 11 -Tekstslide

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      )
s2
s3

Slide 12 -Tekstslide

Homework
• Do §3.4: S25, 27, S28, 28, 29

• Correct your answers with the Solutionsbook and a red pen

Slide 14 -Tekstslide

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

Slide 15 -Tekstslide

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

Slide 16 -Tekstslide

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

Slide 17 -Tekstslide

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

Slide 18 -Tekstslide

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)

Slide 19 -Tekstslide

What did you learn today?