CBSE Class 7 Answered
Considering the equal pair of corresponding angles, prove that each pair of alternate interior angles are equal.
Asked by Topperlearning User | 06 May, 2013, 01:48: AM
Expert Answer
Consider the figure shown below:
Here, t is a transversal that cuts lines m and p. Also,
1 = 5 ; 2 = 6 ; 3 = 7 ; 4 = 8
(pair of corresponding angles)
Now
1 = 3 (vertically opposite angles)
and1 = 5 (pair of corresponding angles)
Thus,
3 = 5 (pair of alternate interior angles)
Similarly we can show that,4 = 6
So, we get the statement as :
"If two parallel lines are cut by a transversal, each pair of alternate interior angles are equal."
Here, t is a transversal that cuts lines m and p. Also,
1 = 5 ; 2 = 6 ; 3 = 7 ; 4 = 8(pair of corresponding angles)
Now
1 = 3 (vertically opposite angles)and
1 = 5 (pair of corresponding angles)Thus,
3 = 5 (pair of alternate interior angles) Similarly we can show that,
4 = 6So, we get the statement as :
"If two parallel lines are cut by a transversal, each pair of alternate interior angles are equal."
Answered by | 06 May, 2013, 03:48: AM
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