State the property that is used in each of the following statements?
If $∠ 4 = ∠ 5 = 180^{o}$ then $a | | b$ .

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Solution

We know that from "ALTERNATE INTERIOR ANGLE PROPERTY",

Interior angles on the same side of traversal are supplementary.

when $∠ 4 + ∠ 5 = 180^{\circ}$

$∴ a ∥ b$

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a | | b

∠ 1 = ∠ 5

∠ 4 = ∠ 6

a | | b

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

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