Download Interior Angles theorem for Quadrilaterals

INTERIOR ANGLES
THEOREM FOR
QUADRILATERALS
By: 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.
5
2
3
6
4-2=2(180)
=360 degrees
3-2=1(180)
=180 degrees
7
1
8
4
2
3
4
5
6
6-2=4(180)
=720 deegres
There 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
C
B
D
AB is congruent to CD
So AC is congruent to BD
Theorem 6-3-2
If 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 6-3-3
If the two pairs of opposite angles are congruent then the quadrilateral
is also a parallelogram
Converse: If a quadrilateral is also a parallelogram then the two pairs of
opposite angles are congruent.
B
C
A
D
<A is congruent to <C
<B is congruent to <D
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.
E
F
D
G
Diagonals bisect each other
<D is congruent to <F
<G is congruent to <E
B
C
A
D
AD is congruent to BC
AB is congruent to CD