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 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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