What theorem did we prove using similar right triangles.

Pythagoras's theorem

Step-by-step explanation:

In the given drawing, there are three right triangles (two smaller triangles formed inside one right triangle), which are;

1) The smallest right triangle with side lengths 'b', 'f', and 'd'

2) The intermediate right triangle with side lengths 'f', 'a' and 'c - d'

3) The right triangle ΔABC containing the other two with side lengths, 'a', 'b', 'c'

By trigonometric ratio we have;

1/cos(B) = a/(c - d) = c/a

By cross multiplication, we get

a² = c² - c·d

Similarly, we have;

The vertex angle for the small right triangle at C = ∠B

1/sin(B) = b/d = c/b

∴ b² = c·d

Therefore, adding the values of 'a²', and 'b²' together, we get;

a² + b² = c² - c·d + c·d = c²

Therefore;

a² + b² = c² which is Pythagoras's theorem.

no

step-by-step explanation:

fabric (square meters)                   cloaks

7                                                           21

4/3                                                         4

step-by-step explanation:

we are told that harry needs 2 square meters of fabric for every 6 wizard cloaks he makes.

1. first of all we will find how many cloaks can be made from 1 square meter of fabric by dividing 6 by 2.

we can see that 3 cloaks can be made from 1 square meter of fabric. now we will multiply 3 by 7 to find number of cloaks made from 7 square meters of fabric.

therefore, harry will make 21 cloaks from 7 square meters of fabric.

2. let us find how many square meters of fabric will be needed to make 4 cloaks.

first of all we will find fabric needed for 1 cloak by dividing 2 by 6.

we can see that fabric needed for 1 cloak is   square meter. now we will multiply   by 4 to find fabric needed for 4 cloaks.