Prove: the median of a trapezoid equals half the sum of its bases.

(fill in the blanks of the equation in the second picture with the correct number/letter/sign based off the first picture.)

1)

We know that the coordinates of M are:

2)

and the coordinates of N are:

3)

Now, in order to find MN we need to find the length of the line segment MN.

We know that the length of the line segment AB with end points A(a,b) and B(c,d) is given as:

Hence, the length of the line segment MN is:

Hence,

4)

Now, end points of A are (0,0) and B are (a,0)

Hence, AB is given as:

Hence,\

AB=a

5)

Now, CD has end-points as:

C(b,c) and D(d,c)

Hence,

Hence,

CD=d-b

6)

The other form of representing MN is:

25

step-by-step explanation:

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).