5.7 The Structure of a Proof

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Solved 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.

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