Geometry Lesson 6 – 6 Trapezoids and Kites Objective: Apply properties of trapezoids. Apply...
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Transcript of Geometry Lesson 6 – 6 Trapezoids and Kites Objective: Apply properties of trapezoids. Apply...
GeometryLesson 6 – 6
Trapezoids and Kites
Objective:Apply properties of trapezoids.
Apply properties of kites.
TrapezoidWhat is a trapezoid?
A quadrilateral with exactly one pair of parallel sides.Bases – the parallel sidesLegs – the nonparallel sidesBase angles – the angles formed by the base and
one of the legs
Isosceles trapezoidcongruent legs
Theorem
Theorem 6.22 If a trapezoid has one pair of congruent
base angles, then it is an isosceles trapezoid.
The speaker shown is an isosceles trapezoid. If m FJH = 85, FK = 8 in. and JG = 19 in. Find each measure.
KH
FGHm
85
8 in19
85
95
95
FH = JGFH = 19FK + KH = 19
8 + KH = 19
KH = 11
Quadrilateral ABCD has vertices A (-3, 4) B (2, 5) C (3, 3) and D (-1, 0). Show that ABCD is a trapezoid and determine whether it is an isosceles trapezoid.
To be a trapezoid the quad must have one set of parallel sides.Slope of AD = -2 Slope of BC = -2The figure is a trapezoid (AB and DC obviously not parallel)
To be isosceles the diagonals must be congruent. 1.6373433 22 AC
8.5340512 22 BD
Trapezoid ABCD is not an isosceles trapezoid.
Quadrilateral QRST has vertices
Q(8, -4) R(0, 8) S(6, 8) T (-6, -10). Determine whether it is an isosceles trapezoid.
Slope of QR = 3/2 Slope of TS = 3/2
Slope of RS = 0Slope of QT = 3/7
Since one pair of parallel sides QRST is a trapezoid.
2.123721488468 22 QS
0.1910636010860 22 RT
Trapezoid QRST is not an isosceles trapezoid.
Midsegment of a Trapezoid
Midsegment of a trapezoidThe segment that connects the midpoints
of the legs of the trapezoid.
TheoremTrapezoid Midsegment TheoremThe midsegment of a trapezoid is parallel
to each base and its measure is one half the sum of the lengths of the bases.
In the figure segment LH is the midsegment of trapezoid FGJK.
What is the value of x?
KJFGLH 2
1
2.182
115 x (2)(2)
30 = x + 18.2
11.8 = x
Trapezoid ABCD is shown below. If FG II AD, what is the x-coordinate of point G?
G is the midpoint of segment DC.
2
04,
2
201G
2,5.10G
The x-coordinate is 10.5
TheoremTheorem 6.25 If a quadrilateral is a kite, then its diagonals are
perpendicular.
Where else have learned about the diagonals being perpendicular?Square & Rhombus
Why does this work for all 3 figures? Is a Square and a Rhombus considered a Kite?
TheoremTheorem 6.26 If a quadrilateral is a kite, then exactly one
pair of opposite angles is congruent.
If FGHJ is a kite, find the measure of angle GFJ
Kites have exactly one pair of opposite congruent angles
x x
2x + 128 + 72 = 360
2x + 200 = 3602x = 160
x = 80
80GHJm
If WXYZ is a kite, find ZY.
(PZ)2 + (PY)2 = (ZY)2
82 + 242 = (ZY)2
640 = (ZY)2
ZY640 Remember to simplify!
ZY1064 ZY108
If BT = 5 and TC = 8, find CD.
5 8
(BT)2 + (TC)2 = (BC)2
52 + 82 = (BC)2
89 = (BC)2
BC89BC = CD
CD89