Geometry
Name_________________________
Geometry – Quadrilaterals Day 4
1. What is the sum of the interior angles of a quadrilateral?
For what value of x is the quadrilateral a parallelogram?
2.
3.
5x + 3
7x - 5
(x + 19)
Find the value of x.
4.
(3x - 13)
5.
40
140
45
x
138
86
x
77
59
2x
Find the sum of the measures of the interior angles of the indicated convex polygon.
6. octagon
7. 19-gon
The sum of the measures of the interior angles of a convex polygon is given. Classify the polygon by
the number of sides.
8. 3960°
9. 1620°
10. Put an X in the box if the shape always has the given property.
Property
Parallelogram
Rhombus
All sides are 
Both pairs of opp. sides are 
Both pairs of opp. sides are
All angles are 
Diagonals are 
Diagonals are 
Diagonals bisect each other
***** STOP ****
Square Rectangle
Today, we will understand Trapezoids, Kites and Special Quadrilaterals
And By the end of class today,
you will be able to find side lengths, angles, and midsegments.
Trapezoids & Kites / Special Quadrilaterals
trapezoid –
bases –
legs –
isosceles trapezoid –
If a trapezoid is isosceles, then each pair of base angles is congruent.
If a trapezoid has a pair of congruent base angles, then it is an isosceles trapezoid.
A trapezoid is isosceles if and only if its diagonals are congruent.
midsegment –
about a midsegment…
- parallel to each base
- half the sum of the lengths of the bases
Examples
Find MN in each trapezoid.
1.
12 in.
2.
M
N
23 ft.
M
N
27 ft.
28 in.
3. Find the unknown angle measures.
B
C
mB 
mC 
m D 
57
A
D
kite –
about a kite…
(properties of a kite)
- diagonals are perpendicular
- exactly one pair of opposite angles are congruent
E
3. Find m  D in the kite shown at the right.
124
F
D
80
G
4. RSTV is a kite. Find the mV.
R
V
80
S
T
Breakdown of Special Quadrilaterals!!
Quadrilateral
Parallelogram
Rhombus
Rectangle
Square
Trapezoid
Isosceles Trapezoid
Kite