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 15PSC
To determine

To prove: The two given line segments AD and BC are congruent

Expert Solution & Answer
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Explanation of Solution

Given information:

Two given lines (AD&BC) intersect at one point (E)

One given line (AC) is perpendicular to the given planes (m & n)

Another given line (BD) is perpendicular to the given planes (m & n)

Formula used:

Congruency means same shape and same size

Congruent Parts of Congruent Triangles are Congruent

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:

  ACm & n and BDm & n .......... given

  ACD=BDC=90° ........... perpendicular lines from right angles

  AC¯BD¯ ........... ACm & n and BDm & n , given

  CD¯AB¯ ............ reflexive property

  ΔACDΔBDC .......... SAS criteria

  AD¯BC¯ .......... Congruent Parts of Congruent Triangles are Congruent

Hence proved

Chapter 6 Solutions

Geometry For Enjoyment And Challenge

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