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Choose point D on the shorter of AC or BC. | Common Notion 5 along with the implicit assumption that points exist on lines via Definitions 2, 3 and 4. |

Construct new point E on AB so that CE is equal to CD. | Proposition 3, Definitions 17 and 4. |

Construct F so that F is the vertex of the equilateral triangle FDE on DE. | Proposition 1 |

Construct FC, DF and EF. | Postulate 1 |

Notice that DF=EF. | Definition 20 |

Therefore angle DCF equals angle ECF. | Proposition 8 |

Hence DCF and ECF are right. | Definition 10 |