Question

Which segments are parallel?

Select each correct answer.

AB
EF
GH
CD

Answer 1

`\sf \overline{AB}`

`\sf \overline{EF}`

`\sf \overline{GH}`

Explanation:

In order to determine the parallel lines, the sum of co interior angle is 180°.

Note: Co-interior angles are two angles that are both inside a pair of parallel lines and on the same side of a transversal. They are also called consecutive interior angles or same-side interior angles.

Now,

Let's check the Co-interior angles.

For Upper one:

47° + 133° = 180°

180° = 180°

Since it is true. So

`\sf \overline{AB} \:|| \: \overline{EF}`

Similarly

For lower one:

34° + 133° = 180°

167° = 180°

Since it is not true. So

`\sf \overline{AB} \: \cancel \: \overline{EF}`

Similarly we can determine parallel lines by alternate iinterior and exterior angle.

In this case, we use alternate exterior angles.

Alternate exterior angles are two angles that are outside a pair of parallel lines and on opposite sides of a transversal.

They are always congruent, or equal in measure.

Over here:

`\sf \angle E \cong \angle H` externally so,

`\sf \overline{EF} \: || \: \overline{GH}`

Therefore, Parallel segments are:

`\sf \overline{AB}`

`\sf \overline{EF}`

`\sf \overline{GH}`