Question

One proof paragraph for 50 pts!

Answer 1

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Explanation:

1. Parallel lines t and g are cut by transversal c. Angles 1 and 9 are corresponding angles when two parallel lines t and g are cut by transversal c. By corresponding angles theorem, corresponding angles are congruent.

2. Parallel lines c and d are cut by transversal g. Angles 9 and 14 are same-side exterior angles when two parallel lines c and d are cut by transversal g. By same-side exterior angles theorem, same-side exterior angles are supplementary (add up to 180°).

3. By substitution property.

Answer 2

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Explanation:

1. Parallel lines t and g are cut by transversal c. Angles 1 and 9 are corresponding angles when two parallel lines t and g are cut by transversal c. By corresponding angles theorem, corresponding angles are congruent, so

`\angle 1\cong \angle 9`

2. Parallel lines c and d are cut by transversal g. Angles 9 and 14 are same-side exterior angles when two parallel lines c and d are cut by transversal g. By same-side exterior angles theorem, same-side exterior angles are supplementary (add up to 180°), so

`\angle 9+\angle 14=180^(\circ)`

3. By substitution property,

`\angle 1+\angle 14=180^(\circ)`