Complete the following proof.

Prove: In an equilateral triangle the three medians are equal.

Step-by-step explanation:

In the figure attached,

ΔABC is an equilateral triangle,

Sides AB = BC = AC and points P, Q, and R are the midpoints of these sides respectively.

If the coordinates of A(0, 0), B(2a, 0) and C(a, b)

AB = 2a

AC =

Since AB = AC

2a =

4a² = a² + b²

3a² = b²

Therefore, ordinate pairs representing midpoints of AB, BC and AC will be

P = =(a, 0)

Q = =

R = =

Now we will find the lengths of medians with the help of formula of distance between two points (x, y) and (x', y')

d =

AQ =

     =

     =

     =  [Since b² = 3a²]

     =

BR =

     =

     =

     =

     =

CP = b =

Therefore, AQ = BR = CP =

Hence, medians of an equilateral triangle are equal.

Hi! Please refer to the image attached. I promise this is a real answer, I got this question right on mine. :D

Good luck!

answer:  

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

which is the required equation for finding the value of x,

fwms@lil_ben06

step-by-step explanation: