MHB Proving Two Triangles are Congruent

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Two triangles are congruent if they meet specific conditions: Side-Angle-Side (SAS), Side-Side-Side (SSS), and Angle-Side-Angle (ASA). The discussion emphasizes using the SSS condition to demonstrate congruence by finding equal corresponding sides. Additionally, supplementary angles can be utilized to establish congruence in another triangle. The focus is on applying these principles to prove triangle congruence effectively. Understanding these conditions is essential for solving geometric problems involving triangles.
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What are the three conditions for two triangles to be congruent?

-Dan
 
topsquark said:
What are the three conditions for two triangles to be congruent?

-Dan
SAS, SSS and ASA?
 
bearn said:
SAS, SSS and ASA?
Good! Now, try for SSS on the first one. Is there any way you can show that BN = GI? For the second one, do the same trick but now you have a couple of supplementary angles to work with. Give it a try.

-Dan
 

Thread 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
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