Can anyone fill this sheet, i'm too confused by this subject and don't understand it. any would be much appreciated.

Question 1

Two triangles are said to be similar, if their sides are proportional and the corresponding angles are equal.

In the given figures, it is given that one of the angles is 80 degrees. So, the corresponding angle in the another triangle is also 80 degrees.

Also, please note that the triangles are isosceles.

We know that, in an isosceles triangle, the angles opposite to the equal sides are equal.

The equal angles are b and b.

By the angle-sum property, we have:

b + b + 80 = 180

2b + 80 = 180

2b = 180 - 80 = 100

b = 50 degrees.

Similar shapes have the same angles.

Question 2:

Even though the length of the second cuboid is twice the length of the first one, no information is given about the breadth and height.

Let b, c be the breadth and height of the first cuboid and B, H be the breadth and height of the second cuboid.

Now, we have two cases.

Case 1:  b = B and h = H

In this case, the volume of the first cuboid is length × breadth × height

= lbh

Volume of second cuboid = (2l) × b × h = 2lbh

So, Simon is correct about the volumes.      

Case 2:  b ≠ B or h ≠ H        

In this case, clearly the volumes will be different and Simon is wrong.

Question 3:

By Basic Proportionality Theorem and from corresponding part of similar triangles,

x = y

or x : y = 1 : 1

Question 4:

Since the jugs are irregular shapes, it is impossible to find their volumes only with known height.