# Math

posted by Rayna

1 the mystery shape has at least 2 lines of symmetry
2 at least 1 of its diagonals is also a line of symmetry
3 it has has at least 1 obtuse angle
4 at least 3 of its angles are congruent
5 its total angle measure is between 100 degrees and 1,000 degrees
A. square
B. rhombus
C. equilateral triangle
D. regular hexagon
E. trapezoid
F. regular octagon
what do you think? Is this right?

1. MathMate

A, C. does it have an obtuse angle?
E. Does it have an axis of symmetry along one of its diagonals?, or in fact, any line of symmetry?
B. Does it have 3 angles congruent?

2. Rayna

When I asked if this is right I mean is the answers A-F right. My answer are A: square, B: rhombus, C: equilateral triangle, D: regular hexagon, E: trapezoid, and F: regular octagon.

3. MathMate

Have you made a choice (or more) out of the 6 or do you believe that all of A to F qualify as answer for the mystery shape?

4. Rayna

So you are telling me that there can only be one answer to this. If so then I chose rhombus to be my answer. Am I right?

5. MathMate

I gave you some hints:
"A, C. does it have an obtuse angle?
E. Does it have an axis of symmetry along one of its diagonals?, or in fact, any line of symmetry?
B. Does it have 3 angles congruent? "

You would have to go through every one of the properties against each possible answer (A - F). An answer that does not satisfy even one of the conditions (properties) will no longer be a candidate.

I have two candidates left for the final answer. Tell me which ones you've got.

For example, for A:
1. Does a square have at least two lines of symmetry? yes (continue)
2.Does a square have at least one of its diagonals as a line of symmetry? yes (continue)
3. Does a square have at least one obtuse angle? No (Stop, and cross out square as a possible answer).

Continue this questioning for all the other shapes from B to F.

6. Rayna

Okay I went through the whole thing and this is what I came up with the answer to this is Trapezoid. Am I right?

7. MathMate

Hint: "angle" in conditions 3-5 refers to the interior angle of a polygon.

Hint: The trapezoid does not satisfy conditions 2 (line of symmetry along diagonal) and 4 (3 congruent angles).

Hint: I have looked through the conditions many times, and I still find two of the 6 choices that satisfy all the conditions.

Finally, make sure you understand perfectly all the terms used in the conditions. If there is doubt, post.

8. Rayna

why do you say that you still find two of the 6 when there is only one answer for it. I can only come up with either a regular hexagon or a regular octagon. A square, rhombus, trapezoid, and equilateral triangle does not work on these.

9. MathMate

Good, you would have to choose bewteen an octagon and a hexagon.

You probably missed the same condition as I did and ended up with two answers instead of one.

Check the last condition:
"5 its total (interior) angle measure is between 100 degrees and 1,000 degrees"
and you'll end up with only one choice.

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