State the property used in each of the following statements in context of the figure given here
If $∠ 4 + ∠ 5 = 180 °$ then $a ∥ b$ .

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Solution

The sum of co-interior angles are $180 °$ only when two lines are parallel and cut by a transversal.
Since, $∠ 4 + ∠ 5 = 180 °$ then lines must be parallel.
Hence, If $∠ 4 + ∠ 5 = 180 °$ then $a ∥ b$ .

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Question 1 (iii)
State the property that is used in each of the following statements:

If $∠ 4 + ∠ 5 = 180^{\circ}$ , then a||b.

?

a ∥ b,

∠ 1 = ∠ 5

∠ 4 = ∠ 6,

a ∥ b

∠ 4 + ∠ 5 = 180^{\circ},

a ∥ b

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

State the property that is used in each of the following statements?

(i) If $ a//b$, then $ \angle 1=\angle 5$.

(ii) If $ \angle 4=\angle 6$, then $ a//b$.

(iii) If $ \angle 4+\angle 5=180°$, then $ a//b$.

∠ 4 = ∠ 5 = 180^{o}

a | | b

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