Prove that EF // GH?

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2 Answers
Feb 5, 2018

As explained

enter image source here

Explanation:

#EhatXY = WhatXF = color(red)(130^0# as they are verically opposite angles

#HhatYX = 180 - GhatYX = 180 - 50 = color(red)(130^0# as GH line is

intersected by WZ and a straight will have #180^0#

Similarly, FhatXY = 180 - EhatXY = 180 - 130 = 50^0#

Now you can see,
#FhatXY + XhatYH = 50 + 130 = 180^0#

Which proves #vec(EF), vec((GH)# are parallel.

When two lines are parallel and cut by a transversal,

  1. Corresponding angles are equal

#EhatXW = GhatYX =50^0#

Likewise, #HhatYZ = FhatXY = 50^0#

#WhatXF = XhatYH = 130^0#

#EhatXY = GhatYZ = 130^0#

  1. Alternate angles are equal

#EhatXW = HhatYZ = 50^0, FhatXY = GhatYX = 50^0#

Feb 5, 2018

See explanation.

Explanation:

WZ= a straight line.
:.1#80^@-130^@=50^@=angleFxZ#
GH= a straight line
#:.180^@-50^@=130^@=angleHyZ#

#angleFxZ=angleGyW#---alternate interior #angles#

If thealternate interior #angles#, the#angles #that are on opposite sides of the transversal WZ and inside the parallel lines are equal, then the lines are parallel. #:. #EF//GH