Geometry For Enjoyment And Challenge
Geometry For Enjoyment And Challenge
91st Edition
ISBN: 9780866099653
Author: Richard Rhoad, George Milauskas, Robert Whipple
Publisher: McDougal Littell
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Chapter 6.2, Problem 9PSB
To determine

To prove: The given point P is equidistant from other two given points, i.e., B and C

Expert Solution & Answer
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Explanation of Solution

Given information:

Given line segment is perpendicular to plane, i.e., PA¯s and

Given point (P) is equidistant from B and C

Formula used:

Congruent Parts of congruent Triangles are Congruent

Reflexive property

If a line is perpendicular to plane than all line passing through its foot will also be perpendicular to it

Perpendicular lines from right angles are always congruent if any one of them lie in a given plane

Proof:

  PA¯s ........... given

Points P is equidistant from B and C B........... given

  PA¯PB¯ &PA¯PC¯ ........... If a line is perpendicular to plane than all line passing through its foot will also perpendicular to it

  PA¯PB¯ ........... Perpendicular lines from right angles

  PA¯PC¯ ........... reflexive

  ΔPABΔPBC

A is equidistant from B and C.......... congruent Parts of congruent triangles are congruent

Hence proved

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Geometry For Enjoyment And Challenge

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