Scale Factors & Similar Figures

Question 1

What is similarity?

Answer 1

2 figures are similar if one can be enlarged and be identical to the other.

Pairs of corresponding side are in the same proportion. All corresponding angles are the same in both objects.

(TRIANGLE) ABC ~ (TRIANGLE) DEF
This means that triangle ABC is similar to triangle DEF.

Question 2

What is a scale factor and formula?

Answer 2

Factors are multiplied to make a product, for example, 5 & 2 give the product of 10.

Scale factor calculation of how many times bigger or smaller a new image gets compared to the original.

Formula: Scale factor = image length (New) / object length (original).

1st Step: Pick the same side from the new and original triangle
2nd Step: Apply formula.

Magnitude: Height of real statue was 1.77m and fake was to be built with scale factor of 2:1, find the new height.

Step 1: 2/1 = 2
Step 2: 1.77 x 2 = 3.54m
New height is 3.54m.

Question 3

How do you find if a ratio is equivalent or not?

Answer 3

Use cross multiplication

5 : 12
? : 36

5 x 36 = 180
180 / 12 = 15
? = 15

Question 4

What are ratios?

Answer 4

Ratios compare quantities of the same kind and same unit of measurement.
Ratios only contain a whole number.

Question 5

What are some tests for triangle congruence?

Answer 5

AAA = Angle, Angle, Angle = All corresponding angles are equal in size.
SSS = Side, Side, Side = Corresponding sides are in the same ratio.
SAS = Side, Angle, Side = 2 pairs of corresponding sides same ratio and included angle.
RHS = Right, Hypotenuse, Side = Both right angles, hypotenuse and one other pair of sides are corresponding.

Question 6

Question -

A 1.5m pole casts a shadow 3m long. Find the height of the nearby building that casts a 15m long shadow.

Answer 6

Step 1: Find scale factor by dividing both length of shadows.
15 / 3 = 5 (Scale factor)
Step 2: Multiply the scale factor by the length of the pole.
1.5 x 5 = 7.5m

Height = 7.5m

Question 7

What are congruent figures?

Answer 7

Congruent figures have the same size and shape.

If two figures are congruent then one of them can be transformed by using rotation, reflection or translation to match the other figure exactly.

If triangle (ABC) is congruent to triangle (DEF) we write,
ABC = DEF (Equals has one more line). This is called a congruence statement.