If a line intersects two sides of a triangle, then it forms a triangle that is similar to the given triangle. always sometimes never

Sometimes.

Step-by-step explanation:  The condition is not always true. As explained in the figure attached, In triangle AB, line MN is not parallel to the side BC but in triangle DEF, line PQ is parallel to the side EF. We can see that triangle AMN is not parallel to triangle ABC but triangle DPQ is similar to triangle DEF. Thus, for the triangles to be similar, the line should be parallel to the third side of the triangle with which the line is not intersecting.

Thus, it is sometimes true.

table 1

step-by-step explanation:

1-16

2-32

4-64

8-128

all multiples of 16

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).