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4.4 The Equidistance Theorems

I can recognize the relationship between equidistance and perpendicular bisection. Day 5. 4.4 The Equidistance Theorems. 1. Prove the following:. 2. If you had to guess, what would equidistant mean? (Break down the word) 3. What does perpendicular mean and what does bisection mean?

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4.4 The Equidistance Theorems

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  1. I can recognize the relationship between equidistance and perpendicular bisection. Day 5 4.4 The Equidistance Theorems 1. Prove the following: 2. If you had to guess, what would equidistant mean? (Break down the word) 3. What does perpendicular mean and what does bisection mean? 4. What do they mean when they are put together?

  2. 4.4 The Equidistance Theorems The distance between two objects is the length of the shortest path joining them. Postulate: A line segment is the shortest path between two points. Distance Formula between two points : Ex 1. Find the distance between (1,9) and (4,5)

  3. Perpendicular Bisector • Defn: The perpendicular bisector of a segment is the segment that is perpendicular to it and also bisects it. CD is the perpendicular bisector

  4. Equidistance • Defn: Two points are equidistant from a third point if they are the same distance from that point. A B C B is equidistant from A and C because B is the same distance from A as it is from C

  5. The equidistance theorems If two points are equidistant from the endpoints of a segment then they form the perpendicular bisector of that segment. • If equidistant , then bisector. • If a point is on the perpendicular bisector of the segment then it is equidistant from the endpoints of the segment. • If bisector, then equidistant.

  6. Example 1 • Given: , C mdpt. of • Prove: B A K C

  7. Example 2 • Given: • Prove: ∠PRI≅∠PNI P I R N T

  8. Example 3 • Given: , • Prove: S H A P E

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