Proving Perpendicular/parallel. Chapter 3

Question 1

If two parallel lines are cut by a transversal, which angles are congruent?

Answer 1

Corresponding, alternate exterior and interior, and consecutive interior angles

Question 2

Alternate interior angels theorem

Answer 2

If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent

Question 3

Alternate exterior angles theorem

Answer 3

If two parallel lines are cut by a transversal, then the pairs of alternate exterior angels are congruent

Question 4

Consecutive interior angles theorem

Answer 4

If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary

Question 5

Corresponding angles converse

Answer 5

If two lines are cut by a transversal so the corresponding angles are congruent, then the lines are parallel

Question 6

Alternate interior and exterior converse

Answer 6

If two lines are cut by a transversal so the alternate exterior and interior angels are congruent, then the lines are parallel

Question 7

Consecutive interior angles converse

Answer 7

If two lines are cut by a transversal so the consecutive interior angles are supplementary, then the lines are parallel

Question 8

Perpendicular postulate

Answer 8

1. If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular.
2. If two lines are perpendicular, then they intersect to form 4 right angles
3. If two sides of adjacent acute angles are perpendicular, then the angles are complementary
4. If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other
5. If two lines are perpendicular to the same line then they are parallel