Download Bases

Identify the type of quadrilateral.
1.
3.
2.
4.
1
Geometry
Section 6.5 ­ Trapezoids and Kites
Definitions
base
Trapezoid ­A quadralateral with exactly one pair of parallel sides.
leg
leg
Bases ­ The parallel sides.
base
Base Angles ­ The two pair of angles with
the included base.
Legs ­ The non parallel sides.
Isosceles Trapezoid ­ A trapezoid with congruent legs.
Theorem 6.14
A
B
If a trapezoid is isosceles, then
congruent
each pair of base angles is ________.
Theorem 6.15
If a trapezoid has a pair of congruent base angles, then it is an ______________.
isosceles
trapezoid.
C
D
A B, C D
A
B
C
D
ABCD is an isosceles trapezoid.
Theorem 6.16
A
B
A trapezoid is isosceles if and only if the congruent
diagonals are ___________.
D
C
2
and
Match the statements with the terms that describes them at the right.
1. QR and PS
2. PQ and RS
3. QS and PR
4. Q and S
5. S and P
Q
A. base's
B. legs
C. diagonals
D. base angles
E. opposite angles
R
S
P
Complete the statements with always, sometimes or never.
6. A trapezoid is ______ a parallelogram.
7. The bases of a trapezoid are ______ parallel.
8. The base angles of an isosceles trapezoid are ______ congruent.
9. The legs of a trapezoid are _____ congruent.
Find the angle measures of ABCD.
11.
10.
12.
B
A
B
108
132
91
53
A
C
D
C
D
Theorem 6.17
C
B
The midsegment of a trapezoid is parallel to each base and its length is one half the sum of the length of the bases.
M
MN AD BC , MN = 1/2(AD + BC)
N
A
D
Find the length of the midsegment:
7
C
14.
9
B
16.
M
B
A
13.
C
B
M
A
N
13
M
D
A
N
16
D
C
12
22
N
D
Homework:
Page; 359
Problems; 1­27
3
Geometry
Section 6.5 (Day 2)
Definition
Kite ­ A quadralateral with two pair of consecutive congruent sides.
Theorem 6.18
A
If a quadrilateral is a kite, then its perpendicular
diagonals are______________
B
D
C
AC BD
Theorem 6.19
A
If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent
___________.
A C
B
B
D
C
D
Find the indicated measures of the following kites
I
17.
A
16.
B
124
32
C
D
B
18.
A
4 2
2
6
D
118
K
74
T
C
E
m A = _______, m B = _______
AB = _____, AD = ______
m K = _______, m E = _______
4
A
81
D 118
20.
19.
A
M
21
74
B
C
m A = m B = _______
B
7 3 10
A
3
T
H
Homework:
21.
m B = _____, m C = _____
Page; 359
C
D
AB = _____, BD = _____
Problem; 2, 28­39
5