Theorem Thursday 8

Question 1

Parallelogram consecutive angles theorem

Answer 1

If a quadrilateral is a parallelogram then it’s consecutive angles are supplementary

Question 2

Parallelogram opposite angles theorem

Answer 2

If a quadrilateral is a parallelogram then it’s opposite angles are congruent

Question 3

Parallelogram opposite sides theorem

Answer 3

If a quadrilateral is a parallelogram then it’s opposite sides are congruent

Question 4

Polygon exterior angles theorem

Answer 4

The sum of the measures of the exterior angles of a convex polygon one angle at each vertex is 360 degrees

Question 5

Corollary to the polygon interior angles theorem

Answer 5

The sum of the measures of the interior angles of a quadrilateral is 360 degrees

Question 6

Polygon interior angles theorem

Answer 6

The sum of the measures of the interior angles of a convex n-gon is (n-2)180

Question 7

Parallelogram diagonals theorem

Answer 7

If a quadrilateral is a parallelogram, then it’s diagonals bisect each other

Question 8

Parallelogram opposite sides converse

Answer 8

If both pairs of opposite sides of a quadrilateral are congruent then the quadrilateral is a parallelogram

Question 9

Parallelogram opposite angles converse

Answer 9

If both pairs of opposite angles of a quadrilateral are congruent then the quadrilateral is a parallelogram

Question 10

Opposite sides parallel and congruent theorem

Answer 10

If one pair of opposite sides of a quadrilateral are congruent and parallel then the quadrilateral is a parallelogram

Question 11

Parallelogram diagonals converse

Answer 11

If the diagonals of a quadrilateral bisect each other then the quadrilateral is a parallelogram

Question 12

Rhombus corollary

Answer 12

A quadrilateral is a rhombus if and only if it has 4 congruent sides

Question 13

Rectangle corollary

Answer 13

A quadrilateral is a rectangle if and only if it has four right angles

Question 14

Square corollary

Answer 14

A quadrilateral is a square if and only if it is a rhombus and a rectangle

Question 15

Rhombus diagonals theorem

Answer 15

A parallelogram is a rhombus if and only if it’s diagonals are perpendicular

Question 16

Rhombus opposite angles theorem

Answer 16

A parallelogram is a rhombus If and only if each diagonal bisects a pair of opposite angles

Question 17

Rectangle diagonals theorem

Answer 17

A parallelogram is a rectangle if and only if it’s diagonals are congruent