1. QuadrilateralsQuadrilaterals
You will learn to identify parts of quadrilaterals and find the
sum of the measures of the interior angles of a quadrilateral.
1) Quadrilateral
2) Consecutive
3) Nonconsecutive
4) Diagonal

2. QuadrilateralsQuadrilaterals
A quadrilateral is a closed geometric figure with ____ sides and ____ vertices.four four
The segments of a quadrilateral intersect only at their endpoints.
Quadrilaterals Not Quadrilaterals
Special types of quadrilaterals include squares and rectangles.

3. QuadrilateralsQuadrilaterals
A
B
C
D
Quadrilaterals are named by listing their vertices in order.
There are several names for the quadrilateral below.
Some examples:
quadrilateral ABCD
quadrilateral BCDA
quadrilateral CDAB
or
quadrilateral DABC

4. S R
Q
P
QuadrilateralsQuadrilaterals
Any two sides, angles, or vertices of a quadrilateral are either __________ or
_____________.
consecutive
nonconsecutive

5. QuadrilateralsQuadrilaterals
S R
Q
P
Segments that join nonconsecutive vertices of a quadrilateral are called
________.diagonals
S and Q are
nonconsecutive
vertices.
diagonalaisSQnonconsecutive
vertices.

6. QuadrilateralsQuadrilaterals
Q
T
S
R
Name all pairs of consecutive sides:
Name all pairs of nonconsecutive angles:
Name the diagonals:
RSandQR STandRS
TQandST QRandTQ
SandQ ∠∠ RandT ∠∠
andQS TR

7. QuadrilateralsQuadrilaterals
D
C
B
A
Considering the quadrilateral to the right.
What shapes are formed if a diagonal
is drawn? ___________two triangles
1
2
3
4
5
6
Use the Angle Sum Theorem (Section 5-2)
to find m1 + m2 + m3 180
Use the Angle Sum Theorem (Section 5-2)
to find m4 + m5 + m6 180
Find m1 + m2 + m3
+ m4 + m5 + m6
180
+ 180
360
This leads to the following theorem.

8. QuadrilateralsQuadrilaterals
Theorem
8-1
The sum of the measures of the angles of a quadrilateral is
____.360
a°
d°
c°
b°
a + b + c + d = 360

9. QuadrilateralsQuadrilaterals
A
D
C
BmA + mB + mC + mD = 360
x + 2x + x – 10 + 50 = 360
Find the measure of B in quadrilateral ABCD if A = x, B = 2x,
C = x – 10, and D = 50.
4x + 40 = 360
4x = 320
x = 80
B = 2x
B = 2(80)
B = 160

10. QuadrilateralsQuadrilaterals