INTERIOR ANGLES THEOREM FOR QUADRILATERALSBy: Katerina Palacios 10-1 T2 Geometry

The interior angles theorem for quadrilaterals says that sum of the angle measures of a triangle has to equal the sum of the angle measures

The formula for this is n-2 (180)

n equals the number of sides.

2

4

3 3-2=1(180)=180 degrees

5 6

7 8

4-2=2(180)=360 degrees

1

2 3

4 5

6

6-2=4(180)=720 deegres

4 theorems of parallelogramsThere are 4 theorems of parallelograms:

Theorem 6-3-1 states that if one pair of opposite sides of a quadrilateral is congruent and parallel then the quadrilateral is also a parallelogram.Converse: If a quadrilateral is also a parallelogram then one pair of opposite sides are congruent and also parallel.

A

B

C

D

AB is congruent to CDSo AC is congruent to BD

Theorem 6-3-2If the two pairs of opposite sides are congruent then the quadrilateral is also a parallelogram.Converse: If a quadrilateral is also a parallelogram then the the 2 pairs of opposite sides are congruent

Theorem 6-3-3If the two pairs of opposite angles are congruent then the quadrilateral is also a parallelogramConverse: If a quadrilateral is also a parallelogram then the two pairs of opposite angles are congruent.

A

B C

D

<A is congruent to <C<B is congruent to <D

How to prove a quadrilateral is also a parallelogram

To prove a quadrilateral is also a parallelogram you have to use the properties and the theorems to determine that. First of all if an quadrilateral has two pair of opposite sides and opposite angles that are congruent than it is also a parallelogram. Since this is one theorem of a parallelogram. Also you know when it is a parallelogram. When diagonals bisect each other. So you have to understand what a parallelogram is in order to know if the quadrilateral is also a parallelogram or not.

Diagonals bisect each other

D

E F

G

<D is congruent to <F<G is congruent to <E

A

B C

D

AD is congruent to BCAB is congruent to CD