: (i) Given, \(a||b\) then \(\angle 1 = ∠5\) [Corresponding angles]
If two parallel lines are cut by a transversal, each pair of corresponding angles are equal in measure.
(ii) Given, \(∠4 = ∠6\), then \(a||b\) [Alternate interior angles]
When a transversal cuts two lines such that pairs of alternate interior angles are equal, the lines have to be parallel.
(iii) Given, \(∠4 + ∠5\) = \(180\degree\) then \(a||b\) [Co-interior]
When a transversal cuts two lines, such that pairs of interior angles on the same side of transversal are supplementary, the lines have to be parallel.
Match the items given in Column I with one or more items of Column II.
Column I | Column II |
(a) A plane mirror | (i) Used as a magnifying glass. |
(b) A convex mirror | (ii) Can form image of objects spread over a large area. |
(c) A convex lens | (iii) Used by dentists to see enlarged image of teeth. |
(d) A concave mirror | (iv) The image is always inverted and magnified. |
(e) A concave lens | (v) The image is erect and of the same size as the object. |
- | (vi) The image is erect and smaller in size than the object. |