Yes, most of them are as if you cut the chair in half both pieces will be mirror image of each other.
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True, but that is a kind of tautological answer. It does not work if you cut it in two along a vertical plane parallel to the back: one part will have the front legs and a bit of the seat while the other will have the back legs, rest of the seat and the back. Not a mirror image. It will work, but only if the chair is cut by a vertical plane that is perpendicular to its back.
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Symmetric
Symmetric Property of Congruence
No. Do your own homework. http://docs.google.com/gview?a=v&q=cache:ZZmsH0jKHH8J:www.cs.utk.edu/~horton/hw1.pdf+For+each+part+give+a+relation+that+satisfies+the+condition+a+Reflexive+and+symmetric+but+not+transitive+b+Reflexive+and+transitive+but+not+symmetric+c+Symmetric+and+transitive+but+not+reflexive%3F&hl=en&gl=us&sig=AFQjCNHGyc1EDhfqj_mu-RV9yTYZZfXl6A
When in a triangle, for angle A, B, C; As the symmetric property of congruence , when ∠A ≌ ∠B then ∠B ≌ ∠A and when ∠A ≌ ∠C then ∠C ≌ ∠A and when ∠C ≌ ∠B then ∠B ≌ ∠C This is the definition of symmetric property of congruence.
The Symmetric Property of Congruence: If angle A is congruent to angle B, then angle B is congruent to angle A. If X is congruent to Y then Y is congruent to X.