Question

Prove that EF // GH?

Answer 1

As explained

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`

Answer 2

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