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 o then a|| b.

Question

State the property that is used in each of the following statements? (i) If a||b, then &#x2220; 1 = &#x2220; 5 (ii) If &#x2220; 4 = &#x2220; 6, then a|| b. (iii) If &#x2220; 4 + &#x2220; 5 = 180 o then a|| b.

Philoid · Accepted Answer

(i) From the above given figure it is clear that,

∠1 = ∠5

This is because a is parallel to b also ∠1 and ∠5 are corresponding angles

Hence,

In these angles are equal due to corresponding angles property

(ii) From the above given figure, it is clear that,

∠4 = ∠6

This is because of the alternate interior angles property

(iii) We have,

From the above given figure, it is clear that,

∠4 + ∠5 = 180^o

Because we know that, the interior angles on the same side of the transversal are supplementary

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 o then 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 ^o then a|| b.