# Points, Lines, and Planes Question

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[math] " Statement " [/math] | [math] " Reason "[/math] |

[math]1. "Let " P " be an arbitrary point on line " [/math] [math] \ \ \ \ \ l " that does not lie on "bar{AC}[/math] | [math]1. "A line consists of an infinite number of points"[/math] |

[math]2. "Construct "bar{AP}" and "bar{CP}[/math] | [math]2. "Two points define a line segment"[/math] |

[math]3. [/math] | [math]3. "Reflexive property"[/math] |

[math]4. B " is the midpoint of " bar{AC}[/math] | [math]4. "Given" [/math] |

[math]5. bar{AB} ~= bar{BC} [/math] | [math]5. "Definition of midpoint"[/math] |

[math]6. l " is the perpendicular bisector of " bar{AC} [/math] | [math]6. "Given"[/math] |

[math]7. ang ABP " and " ang PBC " are right angles" [/math] | [math]7. "Definition of perpendicular"[/math] |

[math]8. ang ABP ~= ang PBC [/math] | [math]8. "All right angles are congruent"[/math] |

[math]9. Delta ABP ~= Delta CBP [/math] | [math]9. ""[/math] |

[math]10. bar{AP} ~= bar{PC} [/math] | [math]10. "Corresponding sides of congruent triangles " [/math] [math] \ \ \ \ " are congruent"[/math] |

[math]11. P " is equidistant from " A " and " C [/math] | [math]11. "Definition of equidistant"[/math] |

## Grade 10 Points, Lines, and Planes CCSS: HSG-CO.C.9

- Consider other points on [math]l[/math], showing the same thing holds true for these other points.
- Redraw the diagram, showing that the results are still true if [math]l[/math] is horizontal and [math]bar{AC}[/math] is vertical.
- State that, if the point on [math]l[/math] lies on [math]bar{AC}[/math], that it is equidistant from points [math]A[/math] and [math]B[/math], due to [math]l[/math] bisecting [math]bar{AC}[/math] (from given information).
- Nothing, it is complete.