Parallel Lines And Polygons

Question 1

Theorems about proving lines parallel

Answer 1

If 2 lines are cut by a transversal such that…..

• a pair of alternate interior angles are congruent
• a pair of interior angles on the same side of the transversal are supplementary
• a pair of alternate exterior angles are congruent

…..then the lines are parallel

Question 2

Theorem: exterior angle of a triangle

Answer 2

The measure of an exterior angle of a triangle is equal to the sum of the measures of the 2 non-adjacent interior angles of the triangle

Question 3

What is the polygon angle sum formula

Answer 3

The sum, S, of the measures of the interior angles of a convex polygon with n sides is given by the formula

S=(n-2) x 180

Question 4

What are the theorems for angles formed by parallel lines?

Answer 4

~ if 2 parallel lines are cut by a transversal, then alternate interior angles are congruent
~ if 2 parallel lines are cut by a transversal, then interior angles on the same side of the transversal are supplementary
~ if 2 parallel lines are cut by a transversal, then alternate exterior angles are congruent

Question 5

What are the properties of a parallelogram?

Answer 5

1) Opposite sides are parallel
2) a diagonal divides a parallelogram into two congruent triangles
3) Opposite sides are congruent
4) Opposite angles are congruent
5) Consecutive angles are supplementary
6) the diagonals bisect each other

Question 6

What are the properties of a rectangle?

Answer 6

1) it is a parallelogram containing one right angle
2) all angles are right angles and is equiangular
3) the diagonals are congruent
4) has all the properties of a parallelogram

Question 7

What are the properties of a rhombus?

Answer 7

1) has all the properties of a parallelogram
2) is equilateral
3) it’s diagonals are perpendicular to each other
4) it’s diagonals bisect its angles

Question 8

What are the properties of a square?

Answer 8

Has all the properties of a rectangle and a rhombus