theorems page two

Question 1

triangle midsegment theorem

Answer 1

The segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half as long as that side

Question 2

triangle longer side theorem

Answer 2

if one side of a triangle is longer than the other side than the opposite angle the larger side is larger than the angle opposite the shorter side

Question 3

triangle larger angle theorem

Answer 3

if one angle of a triangle is larger than another angle then the opposite side of the larger angle is larger than the side opposite the smaller angle

Question 4

triangle inequality theorem

Answer 4

The sum of the lengths of any two sides of a triangle is greater than the length of the third side

Question 5

hinge theorem

Answer 5

if two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second and the third side of the first longer than the third side of the second

Question 6

Converse of the hinge theorem

Answer 6

if two sides of one triangle are congruent to two sides of another triangle and the third side of the first is longer than the third side of the second in the included angle of the first is larger than the included angle of the second

Question 7

polygon interior angles theorem

Answer 7

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

Question 8

corollary to the polygon interior angles theorem

Answer 8

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

Question 9

polygon exterior angle theorem

Answer 9

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

Question 10

parallelogram opposite sides theorem

Answer 10

if a quadrilateral is a parallelogram than its opposite sides are congruent

Question 11

parallelogram opposite angles theorem

Answer 11

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

Question 12

parallelogram consecutive angles theorem

Answer 12

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

Question 13

parallelogram diagonals theorem

Answer 13

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

Question 14

parallelogram opposite sides converse

Answer 14

it’s both pairs of opposite sides of a quadrilateral are congruent then the quadrilateral is a parallelogram

Question 15

parallelogram opposite angles converse

Answer 15

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

Question 16

opposite sides parallel and congruent theorem

Answer 16

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

Question 17

parallelogram diagonals converse

Answer 17

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

Question 18

rhombus corollary

Answer 18

a quadrilateral is a rhombus if and only if it has four congruent sides

Question 19

rectangle corollary

Answer 19

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

Question 20

Square corollary

Answer 20

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

Question 21

rhombus diagnose theorem

Answer 21

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

Question 22

rhombus opposite angles theorem

Answer 22

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

Question 23

rectangle diagonals theorem

Answer 23

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

Question 24

isosceles trapezoid base angles theorem

Answer 24

if a trapezoid is isosceles then each pair of base angles is congruent