Notes 7.4 ­ Trapezoids and Kites.notebook
November 29, 2012
Bellwork
Solve for x.
55o
xo
2xo
25o
Quote ­ "Think big thoughts but relish small treasures."
­ H. Jackson Brown, Jr.
1
Notes 7.4 ­ Trapezoids and Kites.notebook
November 29, 2012
pg. 351 ­ 354 # 15 ­ 43 odd, 55
Assignment 7.3
31. Sometimes(if it is also a rectangle)
33. 18
R 35. 50
37. 1
39. 2√2
41. 45o
P
S
43. 10
S
15. sometimes (if it is also a rhombus)
17. square
19. parallelogram, rectangle, rhombus
and square
Q
21. rhombus and square
~
~
~
23. PQ || RS, PS || QR, PQ=QR=RS=PS
~
~
<P=<R, <Q= <S, PR and QS bisect each
other, PR and QS are perp., PR and QS
are angle bisectors. P
25. rectangle
27. Always; opposite <'s of a parallelogram
B
are congruent.
29. Always; diagonals of a rhombus are < bisectors.
A
C
D
R
Q
55. Rectangle; angles are all right and PR = QS 2
Notes 7.4 ­ Trapezoids and Kites.notebook
November 29, 2012
Notes 7.4 - Trapezoids and Kites
Trapezoid ­ a quadrilateral with exactly one pair of parallel sides
base
leg
leg
base
Isosceles Trapezoid ­ a trapezoid with congruent legs
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Notes 7.4 ­ Trapezoids and Kites.notebook
November 29, 2012
Isosceles Trapezoid Theorems
If a trapezoid is isosceles, then each pair of base angles is congruent.
If a trapezoid has a pair of ≅ base angles, then it is an isosceles trapezoid.
A trapezoid is isosceles if and only if its diagonals are congruent.
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Notes 7.4 ­ Trapezoids and Kites.notebook
November 29, 2012
Quietly Take out a piece of paper please.
Legs
Base <'s
5
Notes 7.4 ­ Trapezoids and Kites.notebook
November 29, 2012
Example 1 ­ PQRS is an isosceles trapezoid. Find m P, m Q, and m R.
S
R
50o
P
Q
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Notes 7.4 ­ Trapezoids and Kites.notebook
November 29, 2012
Trapezoid Midsegment Theorem
Midsegment ­ connects the midpoints of the legs of a trapezoid
C
B
N
M
A
MN AD, MN BC
D
and
1
MN = (AD + BC)
2
7
Notes 7.4 ­ Trapezoids and Kites.notebook
November 29, 2012
Example 2 ­ 8
Notes 7.4 ­ Trapezoids and Kites.notebook
November 29, 2012
Kite ­ a quadrilateral that has two pairs of consecutive congruent sides
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Notes 7.4 ­ Trapezoids and Kites.notebook
November 29, 2012
Theorems About Kites
If a quadrilateral is a kite, then its diagonals are perpendicular.
AC BD
If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent.
A ≅ C, B ≠ D
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Notes 7.4 ­ Trapezoids and Kites.notebook
November 29, 2012
Example 3 ­ Find m G and m J.
11
Notes 7.4 ­ Trapezoids and Kites.notebook
November 29, 2012
Example 4 ­ Find WX.
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Notes 7.4 ­ Trapezoids and Kites.notebook
November 29, 2012
Assignment 7.4
pg. 359 ­ 363 # 11 ­ 23 odd, 29 ­ 33 odd, 36, 52, 55, 61
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