Question

Given: e parallel f and g is a transversal Prove: Angle 1 Is-congruent-to Angle 8 Horizontal and parallel lines e and f are cut by transversal g. On line e where it intersects line g, 4 angles are formed. Labeled clockwise, from uppercase left, the angles are: 1, 2, 4, 3. On line f where it intersects line g, 4 angles are formed. Labeled clockwise, from uppercase left, the angles are: 5, 6, 8, 7. Given that e parallel f and g is a transversal, we know that Angle 4 Is-congruent-to Angle 5 by the alternate interior angles theorem. We also know that Angle 1 Is-congruent-to Angle 4 and Angle 5 Is-congruent-to Angle 8 by the ________. Therefore, Angle 1 Is-congruent-to Angle 8 by the substitution property. corresponding angles theorem alternate interior angles theorem vertical angles theorem alternate exterior angles theorem

Answer 1

c

Explanation:

Answer 2

Fourth option: Vertical Angles Theorem.

Explanation:

The missing picture is attached.

It is important to remember that when parallel lines are cut by another line (This line is called "Transversal"), several angles are formed. These angles can be made into pair of angles that have the same measure.

Vertical angles are the opposite pair of angles that share the same vertex and they are congruent whether the lines are parallel or not.

Knowing this, we can identify in the picture that:

`\angle 1` and
`\angle 4` are opposite and share the same vertex; therefore they are Vertical angles.

`\angle 5` and
`\angle 8` are opposite and share the same vertex; therefore they are Vertical angles.

Then:

`\angle 1\cong\angle 4` and
`\angle 5\cong\angle 8` by the Vertical Angles Theorem.