lexilove262
16.06.2020 •
Mathematics
Complete the following proof.
Prove: In an equilateral triangle the three medians are equal.
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Ответ:
Hi! Please refer to the image attached. I promise this is a real answer, I got this question right on mine. :D
Good luck!
Ответ:
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.
Ответ:
-1/2 because if you solve it would be -.5 but into fraction form it is -1/2