Proving Congruence with Geometry Proofs

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The discussion focuses on proving triangle congruence using geometric proofs, specifically referencing triangles BGE and DGE. Key statements include the congruence of lines GB and GD, angles BGE and DGE, and the reflexive property of line GE. The congruence of the triangles is established through the Angle-Side-Angle (ASA) postulate, leading to the conclusion that corresponding parts of congruent triangles are congruent (CPCTC). A participant questions the discrepancy between the number of statements and reasons, prompting clarification on the missing angle statement. The discussion emphasizes the importance of clearly stating all necessary components in geometric proofs.
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Homework Statement



Statements: 1. Line GB congruent to Line GD
2. Angle BGE congruent to Angle DGE
3. Line GE congruent to Line GE
4. Triangle BGE congruent to Triangle DGE

Homework Equations





The Attempt at a Solution



Statements: 1. Line GB congruent to Line GD
2. Angle BGE congruent to Angle DGE
3. Line GE congruent to Line GE
4. Triangle BGE congruent to Triangle DGE

Reasons: 1. Given
2. Given
3. Reflex
4. ASA
5. CPCTC
 
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Why do you have four statements and five reasons? What does CPCTC stand for?
 
CPCTC = Corresponding Parts of Congruent Triangles are Congruent.
 
Mark44 said:
Why do you have four statements and five reasons? What does CPCTC stand for?

I left out one of the statements: 5. Angle GBE congruent to Angle GDE
 

Thread 'Find the polar form of a complex number'

The working out suggests first equating ## \sqrt{i} = x + iy ## and suggests that squaring and equating real and imaginary parts of both sides results in ## \sqrt{i} = \pm (1+i)/ \sqrt{2} ## Squaring both sides results in: $$ i = (x + iy)^2 $$ $$ i = x^2 + 2ixy -y^2 $$ equating real parts gives $$ x^2 - y^2 = 0 $$ $$ (x+y)(x-y) = 0 $$ $$ x = \pm y $$ equating imaginary parts gives: $$ i = 2ixy $$ $$ 2xy = 1 $$ I'm not really sure how to proceed from here.
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