1. The two triangles are similar because the two pairs of angles are equal, therefore the third angles of both triangles must also be equal.
We can call this the AAA similarity criterion
2. To find QR, we must use ratios between 2 known similar sides of both triangles,

So, QR =1.02
Group like terms , factor out common variable.
(xz+x) + (yz+y)
x(z+1) + y(z+1)
factor out (z+1)
= (z+1)(x+y)
= solution C.
This is the concept of areas of solid materials; the surface area of the cylinder whose radius is 2.5 cm and lateral area is 20 pi cm^2 will be: Surface area of cylinder is given by:
SA=(area of cyclic sides)+(lateral area)
SA=2πr^2+πrl
Area of the cyclic sides will be:
Area=2πr^2
=2*π*2.5^2
=12.5π cm^2
The lateral area is given by:
Area=20π cm^2
Therefore the surface area of cylinder will be:
SA=(12.5π+20π) cm^2
SA=32.5π cm^2
The answer is 32.5π cm^2