*50 points**urgent**plz **
in the figure shown, the angles formed when two parallel lines are cut by a transversal are labeled 1 through 8.

question:

a. prove that any two vertical angles are congruent.

b. one of the two angles from part a has a corresponding alternate interior angle. use the corresponding angles postulate, which says that corresponding angles are congruent, to prove that the angle from part a and its alternate interior angle are congruent.

c. how can you use the proof from part a and the proof from part b to prove that alternate exterior angles are congruent?

See explanation

Step-by-step explanation:

A. Prove that angles 1 and 3 are vertical.

1. - linear pair of angles

2. - linear pair of angles are supplementary

3. - linear pair of angles

4.   - linear pair of angles are supplementary

5.   - substitution property of equality

6. - subtraction property of equality

7. - definition of congruent angles.

So, any two vertical angles are congruent.

B. Prove that angle 3 and angle 5 are congruent.

1. - Corresponding Angles Postulate

2. - definition of congruent angles

3. - vertical angles

4. - definition of congruent angles

5. - substitution property of equality

6.  - definition of congruent angles

So, alternate interior angles are congruent

C. Prove that angle 1 and angle 7 are congruent.

1. - Corresponding Angles Postulate

2. - definition of congruent angles

3. - vertical angles

4. - definition of congruent angles

5. - substitution property of equality

6.  - definition of congruent angles

So, alternate exterior angles are congruent

in problems involving proportions, we can use cross products to test whether two ratios are equal and form a proportion. to find the cross products of a proportion, we multiply the outer terms, called the extremes, and the middle terms, called the means.

hope it