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 2PSA
To determine

To show that sides AB and CD are congruent.

Expert Solution & Answer
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Answer to Problem 2PSA

  AB¯ and CB¯ are congruent.

Explanation of Solution

Given information:

  PBm,APBCPB

Formula used:

The below properties are used:

If a line is perpendicular to a plane, it is perpendicular to every line in the plane that passes through its foot.

Perpendicular angles form right angles.

Right angles are congruent.

Two triangles are congruent by ASA congruence rule.

Corresponding parts of congruent triangles are congruent.

Proof:

It is given that,

  PBm,APBCPB

  Geometry For Enjoyment And Challenge, Chapter 6.2, Problem 2PSA

If a line is perpendicular to a plane, it is perpendicular to every line in the plane that passes through its foot.

  BP¯AB¯ and BC¯

Perpendicular angles form right angles.

  APB and CPB are right angles. 

Right angles are congruent.

  ABP CBP 

By reflexive property, we get

  BP¯   BP¯

By ASA congruence rule, we get

  ΔABP    ΔCBP  

Corresponding parts of congruent triangles are congruent.

  AB¯   CB¯

Chapter 6 Solutions

Geometry For Enjoyment And Challenge

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