Q56 of 93 Page 6

In figure, if x = y and a = b, prove that r || n.
       

Given that r and m are two lines cut by a transversal p and x = y.
x and y are two corresponding angles.
∴ r and m are parallel.
Given that m and n be two lines cut by a transversal q and a = b.
a and b are corresponding angles.
∴ m and n are parallel.
r || m proved and m || n proved.
∴ r || n.

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54 In the given figure lines AB and CD intersect at O. If Ð BOC + Ð BOE = 700 and Ð BOD = 1300, find ഋOC and reflex Ð AOC
 55 Which pair of lines in Fig. are parallel? Give reason.
        57 If p, m, n are three lines such that p || m and n ⊥ p, prove that n ⊥ m. 58 In figure, EF is a transversal to two parallel lines AB and CD. GM ad HL are the bisectors of the corresponding angles EGB and EHD. Prove that GM||HL.