Pearson Lesson 6.6.notebook
February 21, 2017
TRAPEZOIDS AND KITES
Trapezoid ­ a quadrilateral with exactly one pair of parallel sides. The parallel sides are called the bases. The nonparallel sides are called the legs. The two angles that share a base of a trapezoid are base angles. A trapezoid has two pairs of base angles.
An isosceles trapezoid is a trapezoid with legs that are congruent.
1
Pearson Lesson 6.6.notebook
February 21, 2017
Theorem ­ If a quadrilateral is an isosceles trapezoid, then each pair of base angles is congruent.
IF.... TRAP is an isosceles trapezoid
with bases CDEF is an isosceles trapezoid and THEN .... PQRS is an isosceles trapezoid and
. Find 2
Pearson Lesson 6.6.notebook
February 21, 2017
Problem 2: Page 390
Theorem ­ If a quadrilateral is an isosceles trapezoid, then its diagonals are congruent.
IF ...
ABCD is an isosceles trapezoid
THEN ... 3
Pearson Lesson 6.6.notebook
February 21, 2017
Trapezoids also have midsegments. The midsegment of a trapezoid is the segment that joins the midpoints of its legs.
Theorem ­ If a quadrilateral is a trapezoid, then (1) the midsegment is parallel to the bases, and (2) the length of the midsegment is half the sum of the lengths of the bases.
IF .... TRAP is a trapezoid with midsegment THEN .... (1)
(2) is the midsegment of trapezoid LMNP. What is x?
4
Pearson Lesson 6.6.notebook
February 21, 2017
is the midsegment of trapezoid PQRS.
What is x? What is MN?
5
Pearson Lesson 6.6.notebook
February 21, 2017
Kite ­ a quadrilateral with two pairs of consecutive sides congruent and no opposite sides congruent.
Theorem ­ If a quadrilateral is a kite, then its diagonals are perpendicular.
IF ....ABCD is a kite
THEN ....
6
Pearson Lesson 6.6.notebook
February 21, 2017
Quadrilateral DEFG is a kite. What are Diagonals of a kite are perpendicular
Triangle Angle­Sum theorem
So, Quadrilateral KLMN is a kite. What are 7
Pearson Lesson 6.6.notebook
February 21, 2017
CONCEPT SUMMARY RELATIONSHIPS AMONG QUADRILATERALS
2 pair
irs of
no pa l sides
lle
para
Kite
s of p
Quadrilaterals
Only 1
parall pair of
el sid
es
Trapezoid
Isosceles
Trapezoid
aralle
l side
s
Parallelogram
Rectangle
Rhombus
Square
8
Pearson Lesson 6.6.notebook
February 21, 2017
P. 394 7 ­ 38, 47 ­ 52, 57 ­ 62
9