References

IS THE CONVERSE CLAIM TRUE? AND IF IT IS, HOW IS IT PROVEN?


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[2] L. Hoehn, Problem posing in geometry, The Mathematics Teachers 91(1) (1991), 10-14.

[3] S. Brown and M. Walter, The Art of Problem Posing (2nd Edition), Philadelphia: Franklin Institute Press, 1990.

[4] S. Brown and M. Walter, Problem Posing: Reflection and Applications, Hillsdale: NJ: Erlbaum, 1993.

[5] National Council of Teachers of Mathematics, Principle and Standards for School Mathematics, Reston, VA: NCTM, 2000.

[6] The Great Soviet Encyclopedia, 3rd Edition (1970-1979), © 2010 The Gale Group, Inc..

[7] I. S. Gradshtein, I. N. Sneddon, M. Stark and S. Ulam, Direct and Converse Theorems: The Elements of Symbolic Logic (Pure & Direct and Converse Theorems: The Elements of Symbolic Logic), (First Chapter), Burlington: Elsevier Science, 2014.

[8] A. I. Fetisov and Ya. S. Dubnov, Proof in Geometry: With Mistakes in Geometric Proofs (Second Book), Dover Publications, 2006.

[9] R. Lachmy and B. Koichu, Journal of Mathematical Behavior 36 (2014), 150-165.

[10] M. Stupel and D. Ben-Chaim, One problem, multiple solutions: How multiple proofs can connect several areas of mathematics, Far East Journal of Mathematical Education 11(2) (2013), 129-161.

[11] R. Liekin, Multiple proof tasks: Teacher practice and teacher education, ICME Study 19(2) (2009), 31-36.

[12] S. Abu-Saymeh, M. Hajja and H. A. ShahAli, Another Variation on the Steiner-Lehmus Theorem, Forum Geom. 8 (2008), 131-140.

[13] M. Hajja, A short trigonometric proof of the Steiner-Lehmus theorem, Forum Geom. 8 (2008), 39-42.

[14] Online Wikipedia - The Euler’s proof.

https://en.wikipedia.org/wiki/Euler%27s_theorem_in_ geometry

[15] A. Engel, Problem-Solving Strategies (Problem Books in Mathematics), Springer Ed., N.Y., (1991), 291-293.