Question

Determine if triangle DEF with coordinates D (2, 1), E (3, 5), and F (6, 2) is an equilateral triangle. Use evidence to support your claim. If it is not an equilateral triangle, what changes can be made to make it equilateral? Be specific.

Answer 1

@djcool31

Answer 2

@undeadknight26

Answer 3

1st step, get to a graphing site, or use graphing paper to make a coordinate plane

Answer 4

2nd step, graph the coordinates

Answer 5

ok

Answer 6

hold on, let me graph it real quick ;D

Answer 7

3rd step, look at all of the angles, and sides of the triangle, measure the distance between each corner

Answer 8

how do you do that

Answer 9

well, an easy way is just to get a ruler and put it up to the screen, or, if you have a good graphing site or something to use, you can measure the angles. I recommend Geogebra.org

Answer 10

how can I do it with math or showing work

Answer 11

This might help, it's the graph I made, you can look at the angles, and see they're not exactly congruent

Answer 12

I thought that an equilateral just had to have the same lengths

Answer 13

It does, but the angles have to do with the length itself. Angles are what makes triangles, well.. triangles

Answer 14

true so do you know how to do that without a graphing thing

Answer 15

do you have a protractor?

Answer 16

no I need to do it for a flvs question and I don't remaber how to do any of this stuff

Answer 17

if you want to measure the angle of a triangle, I think you need a protractor.. let's see if we can make something up.. First of all, measure the lengths of the sides, tell me what you get, please

Answer 18

So it's like this
a = 4.24
b = 4.12
c = 4.12
So this is an Isosceles triangle

Answer 19

is there a formula to do that with

Answer 20

There probably is, I forgot it, Hold on, i'll look through my notes

Answer 21

ok

Answer 22

cosA = (b^2 + c^2 − a^2) over 2bc
cosB = (c^2 + a^2 − b^2) over 2ca
cosC = (a^2 + b^2 − c^2) over 2ab

So, that's the cosine formula to get angles
When I say 'over 2bc, 2ca or 2ab' I mean it's b^2 + c^2 = a^2
---------------
2bc

Answer 23

i was taught that you use distends formal i know it has a square root in it that is it

Answer 24

Use this formula if you want to get the angle. it's easy.
cosA =b2 + c2 − a2
-----------
2bc
So
cosA = 4.12^2 + 4.12^2 − 4.24^2
------------------------
2 * 4.12 * 4.12

cosA = 16.97 + 16.97 - 17.98
--------------------
33.95

cosA= 15.96
______
33.95
cos A = 0.47010 degrees

if i did that right for A, the angle is 0.47010

I DID round for some of the decimals

Answer 25

Ok

Answer 26

Yep, so, in answer to the actual question, no it is not an equilateral because B and C have the same length, but A is not equal, so it IS an isosceles. The way you could change it to be an equilateral is if you shortened the size of A by 0.12

Answer 27

ok thanks

Answer 28

By the way, D = A, E = B and F = C