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Grade 10 Math · Problem type

What the angle bisector construction guarantees

Use this for “After bisecting ∠AOB with a compass, which statements must be true?”

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Is the statement always true after the construction?
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Assumptions

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The first arc from O cuts the sides at A and B; the equal arcs from A and B cross at P.
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Only what the equal compass openings make equal is guaranteed.
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