Can two triangles not be congruent but five elements in triangle are same
There are 3 sides and 3 angles in triangle. All 3 sides and 3 angles are collectively called 6 elements
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3What's an element? – Oscar Lanzi Sep 30 '23 at 09:48
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4An 8-12-18 triangle and a 12-18-27 triangle share all three angles and two sides. – Gerry Myerson Sep 30 '23 at 10:37
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Are you still here, Adi? Any observations on the comments and/or the answer that has been posted? – Gerry Myerson Oct 04 '23 at 05:56
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Yes answer helped – Oct 04 '23 at 09:29
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You have the option of "accepting" my answer, by clicking in the check mark next to it. But if you still need some clarification, you should tell us what you need. – Gerry Myerson Oct 04 '23 at 21:25
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I'll assume that by "elements" OP means side lengths and angles.
Let triangle $ABC$ have sides $AB$ of length $8$, $BC$ of length $12$, and $AC$ of length $18$. Let triangle $XYZ$ have sides $XY$ of length $12$, $YZ$ of length $18$, and $XZ$ of length $27$.
Then the triangles are similar, since $|AB|/|XY|=|BC|/|YZ|=|AC|/|XZ|=2/3$. So $\angle A=\angle X$, $\angle B=\angle Y$, and $\angle C=\angle Z$.
Also, $|BC|=|XY|=12$, and $|AC|=|YZ|=18$. So, five elements are equal, but the triangles are manifestly not congruent.
Gerry Myerson
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