Concept explainers
(a)
Find the relation between the measures of the odd-numbered
(a)
Answer to Problem 36PPS
Explanation of Solution
Given:
The two levels of the bridge are parallel.
Formula Used:
Alternate Interior Angle Theorem : If two lines are parallel and are cut by a transversal , then the pair of alternate interior angles is congruent.
Corresponding Angle Postulate: If two lines are parallel and are cut by a transversal , then the pair of corresponding angles is congruent.
Calculation:
The following pairs are alternate interior angles and are congruent by Alternate Interior Angles Theorem :
The following pairs are corresponding angles and are congruent by Corresponding Angle Postulate :
So,
(b)
Find the relation between the measures of the even-numbered angles.
(b)
Answer to Problem 36PPS
Explanation of Solution
Given:
The two levels of the bridge are parallel.
Formula Used:
Alternate Interior Angle Theorem : If two lines are parallel and are cut by a transversal , then the pair of alternate interior angles is congruent.
Calculation:
The following pairs are alternate interior angles and are congruent by Alternate Interior Angles Theorem :
The following pairs are alternate interior angles and are congruent by Alternate Interior Angles Theorem :
So,
(c)
Find the relation between the measures of the odd-even numbered angles.
(c)
Answer to Problem 36PPS
All the pairs consisting one odd-even angle are complementary.
Explanation of Solution
Given:
The two levels of the bridge are parallel.
Formula Used:
Consecutive Interior Angle Theorem : If two lines are parallel and are cut by a transversal , then the pair of consecutive interior angles is congruent.
Calculation:
From part (a) and (b) :
Also,
Hence,
So, all the pairs consisting one odd-even angle are complementary.
(d)
Find the geometric term(s) that can be used to relate the two roadways contained by the bridge.
(d)
Answer to Problem 36PPS
Parallel
Explanation of Solution
Given:
The two levels of the bridge are parallel.
Calculation:
From part (a) , (b) and (c) , we can conclude that :
The planes of the two roadways contained by the bridge are parallel.
Chapter 3 Solutions
Geometry, Student Edition
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