5.7 The Structure of a Proof
Ask AISolved Examples
Step 1
Given: Line segment AB.
Step 2
Step 1: Using Postulate 3, draw a circle with center A and radius AB.
Step 3
Step 2: Draw a circle with center B and radius BA.
Step 4
Step 3: Let the circles intersect at point C.
Step 5
Step 4: Join AC and BC (Postulate 1).
Step 6
Proof: AC = AB (Radii of same circle). BC = AB (Radii of same circle). By Axiom 1, AC = BC. Thus AB = BC = CA.
Step 7
Triangle ABC is equilateral.
Final Answer
Constructed and Proved.