State the property that is used in each of the following statements?
(i) If a || b, then ∠1 = ∠5.
(ii) If ∠4 = ∠6, then a || b.
(iii) If ∠4 + ∠5 = 180°, then a || b.
Solution:
We use the concept of parallel lines, alternate interior angles and corresponding angles to solve the problem.
(i) If a || b, then ∠1 = ∠5. are corresponding angles. If two parallel lines are intersected by a transversal, then each pair of corresponding angles are equal.
(ii) If ∠4 = ∠6, then a || b. When a transversal intersects two lines such that if a pair of alternate interior angles are equal then the lines are parallel.
(iii) If ∠4 + ∠5 = 180°, then a || b. When a transversal intersects two parallel line such that pair of interior angles on the same side of the transversal are supplementary, then the lines are parallel.
☛ Check: NCERT Solutions Class 7 Maths Chapter 5
Video Solution:
State the property that is used in each of the following statements? (i) If a || b, then ∠1 = ∠5. (ii) If ∠4 = ∠6, then a || b. (iii) If ∠4 + ∠5 = 180°, then a || b
NCERT Solutions for Class 7 Maths Chapter 5 Exercise 5.2 Question 1
Summary:
The property that is used in each of the following statements (i) If a || b, then ∠1 = ∠5. (ii) If ∠4 = ∠6, then a || b. (iii) If ∠4 + ∠5 = 180°, then a || b are (i)If two parallel lines are intersected by a transversal, then each pair of corresponding angles are equal, (ii) if pair of alternate interior angles are equal then the lines are parallel, (iii) If pair of interior angles on the same side of the transversal are supplementary, then the lines are parallel
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