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6.5 Trapezoids & Kites. Trapezoid. Is a quadrilateral with exactly 1 pair of parallel sides. BASE. base angle. base angle. leg. leg. base angle. base angle. BASE. Trapezoid. A B. C D. If the legs are congruent then the trapezoid is an isosceles trapezoid. Theorem 6.14. - PowerPoint PPT Presentation
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6.5Trapezoids & Kites
Trapezoid
• Is a quadrilateral with exactly 1 pair of parallel sides
Trapezoid
A B
C D
leg
leg
BASE
BASE
If the legs are congruent then the trapezoid is an isosceles trapezoid.
Theorem 6.14•If a trapezoid is isosceles, then each pair of base angles is congruent.
Theorem 6.15•If a trapezoid has a pair of congruent base angles, then it is an isosceles trapezoid.
Theorem 6.16•A trapezoid is isosceles if and only if its diagonals are congruent.
Midsegment•The midsegment of a trapezoid is the segment that connects the midpoints of its legs.
THM 6.17• The midsegment of a
trapezoid is parallel to each base and its length is one half the sum of the lengths of its bases
21 basebase21midsegment
EX 1 Find the length of MN.
13
P Q
M N
S R
10
16
EX 2 Find the value of x.
19 15 17 x
A Kite•A quadrilateral with two pairs of consecutive congruent sides, but opposite sides are not congruent.
Theorem 6.18•If a quadrilateral is a kite, then its diagonals are perpendicular.
Theorem 6.19•If a quadrilateral is a kite, then exactly one pair of opposite angles is congruent.
Ex 3 Find the measure of the sides. Round to the nearest tenth.
LM = 3.6LO = 3.6ON= 5MN = 5
L
M
N
O
2
3 3
4
Ex 4 Find the mL.
110
40
100
L
M
N
O
Ex 5 Find the mL.
3555
135
x
L
M
N
O
Add Trapezoid and Kite to your foldable.
Goal: Identify midsegments and use properties of midsegments of a triangle
Midsegment – a segment that connects the midpoints of two
sides of a triangle.
Midsegment Theorem
A
B
C
X YAC || XY
XY = ½ AC
The segment connecting the midpoints of two sides of a triangle is parallel to the third side and half as long.
Ex 1: UW and VW are midsegments of RST. Find UW and RT.
R
S
T
V
W
U
128
UW = 6
RT = 16
Ex 2: X, Y, and Z are the midpoints of UVW. Complete each statement.
U
X
V WZ
Y
a. If VW = 6a, then XY = ___
b. mWZY = 2b + 1, then mWVU = ______.
c. XZ _______.d. If YZ = c, then UV =
____
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