Evil Symmetry

Geometry Level 2

Bob the minion is learning symmetry because he wants to become the evilest supervillain ever. Gru hands him the following figure as an exercise and asks him to mark all the lines of symmetry.

A Somewhat Squashed Star:

Bob draws the following lines; however he is not sure if he is completely correct. Please help him.

Which of these lines are not lines of symmetry for the given figure? Find the sum of all the incorrect lines.

As an explicit example, if you think lines $2$ and $3$ are not lines of symmetry, then your answer is $2 + 3 = 5$ .

8 3 There are no incorrect lines. 9 10 15 13 5

5 solutions

Pranshu Gaba
Sep 4, 2015

To test whether a given line is a reflectional line of symmetry, we can place a mirror on it. If the original shape is obtained after placing the mirror, then the given line is a line of symmetry. To read more about reflection symmetry, check out the Symmetry wiki.

In the following figure, we place a mirror at the 5 lines we have to test. The light blue region is the mirror image of the original dark blue region. We see that after placing the mirror, only the figure with line 2 looks looks like the original star and all other figures are distorted. Therefore only line 2 is a line of symmetry, and lines 1, 3, 4, 5 are not lines of symmetry. Hence the answer is $1 + 3 + 4 + 5 = \boxed{13}$ $_\square$

Excellent job of making this point clear.

Michael Mendrin - 5 years, 9 months ago

Thank you!! :)

Pranshu Gaba - 5 years, 9 months ago

Michael Mendrin
Sep 3, 2015

It's all a matter of perspective! Trick, tricky, tricky....

Don't get it. Only line 1 and 3 are not the lines of symmetry. Rest all other lines are lines of symmetry.

Vibhor Agarwal - 5 years, 9 months ago

If the 5 pointed star wasn't WARPED, if it was inscribed inside a circle for instance, then all lines 1, 2, 3, 4, 5 would be reflective lines of symmetry. However, the diagram of the 5 pointed star is warped because of "perspective", i.e., it's tilted down.

Michael Mendrin - 5 years, 9 months ago

OK! You must have mentioned something in the question itself.

Vibhor Agarwal - 5 years, 9 months ago

Please have a look at my solution which explains why only line 2 is a reflective line of symmetry.

Pranshu Gaba - 5 years, 9 months ago

But not here

yash dharme - 5 years, 9 months ago

Klarke Allen
Dec 2, 2015

I don't know if you have ever tried this, but folding a star any other way besides arm to arm does not work. So 2 is the only line of symmetry. Add the lines 1, 4, 3, and 5. The answer is 13.

Saarthak Marathe
Sep 9, 2015

The only line of symmetry is line 2.

Hadia Qadir
Sep 8, 2015

1 3 4 5 which would equal 13

Evil Symmetry

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