Concept explainers
(a)
Draw five pair of parallel lines , m and n , a and b , r and s , j and k , and x and y , cut by a transversal t .
(a)
Explanation of Solution
Given:
Calculation:
Draw the lines :
(b)
Record the data in a table of the measures of each
(b)
Explanation of Solution
Calculation:
From part (a), we measure the angles of 1,2,3,4 in each pair of parallel lines :
88 | 92 | 88 | 92 |
60 | 120 | 60 | 120 |
90 | 90 | 90 | 90 |
80 | 100 | 80 | 100 |
30 | 150 | 30 | 150 |
(c)
Make a conjucture about the relationship between the pair of angles formed on the exterior of parallel lines and on the same side of transversal.
(c)
Answer to Problem 41PPS
The pair is supplementary.
Explanation of Solution
Calculation:
From part (a) and (b),
88 | 92 | 88 | 92 |
60 | 120 | 60 | 120 |
90 | 90 | 90 | 90 |
80 | 100 | 80 | 100 |
30 | 150 | 30 | 150 |
So, a pair of exterior angles on the same side of transversal is supplementary.
(d)
Find the type of reasoning did you use to form the conjucture in part (c).
(d)
Answer to Problem 41PPS
Inductive
Explanation of Solution
Calculation:
Since the conjucture was deduced by using the reasoning of certain pattern in all 5 pairs of parallel lines, hence the conjucture was based on inductive reasoning.
(e)
Write a proof of your conjucture.
(e)
Explanation of Solution
Calculation:
To Prove : A pair of exterior angles on the same side of transversal is supplementary.
Proof:
Hence ,
Hence proved.
Chapter 3 Solutions
Geometry, Student Edition
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