Question

Please anyone help me with this!

Answer 1

@nubeer It is better explained here

Answer 2

To find the missing answers

Answer 3

@just.chris

Answer 4

I do not have the book defining the Corollary to the Base Angles Theorem. I am also not completely sure what the question(s) are. It seems to answer them in the chart.

For instance, the base angle theorem states that if tos ides of a triangle are equal then the angles opposite that side are also equal.

Since this is a construction of an equilateral triangle all sides and therefore all angles are equal.

So the first line of the chart is just stating at truth about and equiangular triangle (all of which are also equilateral triangles).

Answer 5

Line two just states the Triangle Sum Teorem which is true for all triangles.

Answer 6

@just.chris what about line two where it states that 'm∠A = m∠B = m∠C' could it be "definition of congruent angles' ?

Answer 7

And since all of the angles are equal, then the sum of the last line of the chart is obvious, yes? Let me know if this is not obvious to you.

Answer 8

In the lines I have to write a proof or a statement

Answer 9

They are asking you to prove theorems? If so, let me think about it a bit, because proofs rely on theorems.

Answer 10

Yes. Complete the following proof that the measure of each angle of an equilateral triangle is 60°.

Answer 11

Ok then, no problem

Answer 12

And btw, the words that are written in bold are written by me, so if they are wrong, please tell me.

Answer 13

Well what I first wrote about the base angles theorem is a proof that equilateral triangles are equiangular as well.

Answer 14

So the first one is correct. Thank you.

Answer 15

No your bold text is correct. or at least I know they are not wrong.

Answer 16

Ok then. thanks :)

Answer 17

So for the "definition" I think it is the same. If all angles are equal/congruent then it is equilateral equiangular triangle.

Answer 18

It might just seem to simple because they just asked it. But it is not wrong.

Answer 19

thanks. simple for the fourth part? I have no idea what m∠A + m∠A + m∠A = _____________

Answer 20

For the last one, as they say, they are doing substitution. YES

Answer 21

Yes but what goes in the dotted line? :(

Answer 22

all the angles are equal so 3 times any angle is ...

Answer 23

3 times the other angles?

Answer 24

m∠A = m∠B = m∠C
m∠A + m∠B + m∠C = 180
so what does the sum of any combination of three of these angles equal?

Answer 25

equal angles?

Answer 26

Yes equal angles.

Maybe is would be easier just to think of it as a math problem, but the algebra works for everything.
a = b = c
a + b + c = 180
Solve for any variable.

Answer 27

Thanks! the proof has three more lines? can you still help me or is it bothering you?

Answer 28

Meaning a + a + a = b + b + b = c + c + c = 180
a = b = c = 60
Works exactly the same for the angles. The algebra rules apply. One of the really cool and fairly unique thinks about algebra, it's rules work for virtually everything.

Answer 29

Are you cool? I got to head out soon.

Answer 30

Oh then no problem thanks anyway for everything :)

Answer 31

Sure I didn't see the other lines. I still have a few minutes if that'll do it they are yours.

Answer 32

Thanks a lot then! I really appreciate it. Here they are

Answer 33

Cool, easy. Just algebra again.

Answer 34

Ok great then! THANKS

Answer 35

OK, m∠A = what?

Answer 36

60 degrees

Answer 37

and 3 x 60 =?

Answer 38

180 degrees

Answer 39

Aye, captain.

Answer 40

wow! thanks!

Answer 41

I think for the next one since we are dealing with an equilateral/equiangular triangle, they are looking for the sum of the angles of the triangle divided by the number of angles.

Answer 42

so 60/3?

Answer 43

no the sum of all the angles divided by 3.

Answer 44

180/3 ?

Answer 45

Yes, I believe that is what they are looking for.
The answer from the "Triangle Sum Theory" divided by 3.

Answer 46

Like this m∠A = 180° ÷ 3 = 60° ?

Answer 47

Yes, sir.

Answer 48

THANKS!!!

Answer 49

Thank you soooooooo much!!!!

Answer 50

The last one is oddly presented. The transitive property is usually expressed
If a = b and b = c then a = c.

What they have is more like the "symmetric property of equality" but since its three terms I guess it could be either.

Answer 51

I gotta run now. Later, RH.

Answer 52

Thank you again so much!!! Have a great day!!! LATER :):):)