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EQUIDISTANCE

EQUIDISTANCE. Geometry Chapter 4.4. Some basics: . A.) ( def ) Distance (between two objects) is the length of the shortest path joining them. B.) ( postulate ) A line segment is the shortest path between two points. Definition of Equidistance:.

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EQUIDISTANCE

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  1. EQUIDISTANCE Geometry Chapter 4.4

  2. Some basics: A.) (def) Distance (between two objects) is the length of the shortest path joining them. B.) (postulate) A line segment is the shortest path between two points.

  3. Definition of Equidistance: • If 2 points P and Q are the same distance from a third point X, then X is said to be _____________from P and Q. EQUIDISTANT

  4. Definition of a Perpendicular Bisector: • A perpendicular bisector of a segment is the line that both _________ and is _____________to the segment. BISECTS PERPENDICULAR

  5. Theorem 24: If 2 points are equidistant from the endpoints of a segment, then they determine the perpendicular bisector of the segment.Abbrev: (PBT)(Perpendicular Bisector Theorem) NEEDED: 2 points equidistant or 2 pairs congruent segments

  6. 1. 2. 3. 4. 5. 6. Given CPCTC (1) Def of =Dist (2) CPCTC (1) Def of =Dist (4) If 2 points are =dist from the endpoints of a segment, then they determine the perpendicular bisector. (3,5) Given: Prove: 6. PBT

  7. Theorem 25: If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. Abbrev: (PBP) (Perpendicular Bisector Property) NEEDED: Perpendicular Bisector of the Segment.

  8. 1. 2. 3. X is =dist from A & B 4. 5. F is =dist from A & B 6. 7. 1. Given 2. Reflexive 3.If a point is on the perp bisector, then it is =dist. (1) 4. Def of =Dist (3) 5. Same as #3 (1) 6. Def of =Dist (5) 7. SSS (2,4,6) Given:Prove: S 3. PBP S S

  9. TRUE/FALSEPRACTICEReady??

  10. 1. E is the midpoint of BC. TRUE

  11. 2. <AEC is a right angle TRUE

  12. 3. E is the midpoint of AD FALSE

  13. 4. TRUE

  14. 5. TRUE

  15. 6. FALSE

  16. 7. FALSE

  17. 8. FALSE

  18. Prove the following statement: The line drawn from the vertex angle of an isosceles triangle through the point of intersection of the medians to the legs is perpendicular to the base.

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