Question

Based on the given statements, which is a valid argument?
@mathstudent55
@surjithayer
@iambatman

Answer 1

Any ideas?

Answer 2

for an equilateral triangle all three sides and all three angles are equal.

Answer 3

I believe it is A. , just like surjithayer mentioned above- "for an equilateral triangle all three sides and all three angles are equal", this is correct. The problem is we weren't told if "all three angles" are equal!

Answer 4

@surjithayer and @mathmate

Answer 5

if all the three sides of a triangle are equal,it implies all the three angles are also equal.

Answer 6

The question itself is a little misleading.

Strictly speaking, a triangle with all three angles congruent is an equiangular triangle, and a triangle with all three sides congruent is an equilateral triangle.

It can be proved that \(all~equiangular~triangles~are~equilateral,~and~vice~versa\).

Perhaps for this reason, the two terms are frequently treated as synonymous.

In the above question which treats them differently, I would have used the correct terms.

Answer 7

By process of elimination I can eliminate option A and option D.

Answer 8

Hmmm...

Answer 9

Thank you mathmate and surjithayer.
@mathmate Yes, it is a bit misleading!

Answer 10

"Equiangular" means all angles are equal.

Etymology of "lateral":
Origin
late Middle English: from Latin lateralis, from latus, later- ‘side.’

So equilateral means all sides are equal.

Does that change your reasoning?

Answer 11

I don't understand, I'm saying:
Option A- False , because they are equal
Option B- I think it's this one.
Option C- I think this is false.
Option D- False, we are only told about 3 sides- not 4.

Answer 12

Option A- *False, because we can conclude they are equal*

Answer 13

Option A is false. I have misread the statement.
You are good so far in eliminating A and D.
Can you elaborate why you chose B?

Answer 14

Based on the given information, we are able to prove she drew a closed figure, in this case a triangle, thus, that eliminates option C.

Answer 15

^Way better explanation!

Answer 16

Yes, the logic is much better! Direct and positive!

Answer 17

\(\color{blue}{\Large\checkmark}{Way~to~go!}\)

Answer 18

Thank you!
@mathmate To conclude do you agree it is option B as well?

Answer 19

Yes, because everything it states corresponds to what is given, so there is no contradiction.

Answer 20

Thank you love ! :)

Answer 21

You're welcome! :)