Question

One proof paragraph for 50 pts!

Answer 1

Answer:

See explanation

Step-by-step 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,

$\angle 1+\angle 14=180^{\circ}$

Answer 2

Answer:

Read Below

Step-by-step 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.