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 3PSA
To determine

To prove: The given line segments RS¯ and RT¯ are congruent

Expert Solution & Answer
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Explanation of Solution

Given information:

A circle with center O lies in plane n

One line segment is perpendicular to plane ‘n’, i.e., RO¯n

Formula used:

Congruency means same shape and same size

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 perpendicular to it

Perpendicular lines always form right angles

Proof:

  RO¯n........... given

  RO¯OS¯  & RO¯OT¯........... (If a line is perpendicular to plane than all line passing through its foot will also be perpendicular to it)

  ROS=ROT=90° ...........Perpendicular lines from right angles

  RS¯RT¯ .............................. Reflexive property

  RO¯RO¯.................Reflexive Property

  ΔROSΔROT SAS criteria is satisfied

  RS¯RT¯.................CPCTC

Hence proved

Chapter 6 Solutions

Geometry For Enjoyment And Challenge

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