Use Properties of Trapezoids and Kites
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Transcript of Use Properties of Trapezoids and Kites
Use Properties of Use Properties of Trapezoids and KitesTrapezoids and KitesChapter 8.5
TrapezoidsTrapezoidsTrapezoids are quadrilaterals
that have 2 parallel sidesThe parallel sides are called the
bases.◦A trapezoid has 1 pair of base
angles.The non-parallel sides are called
the legs.base
baseLeg Leg
Is it a trapezoid?Is it a trapezoid?Are the bases parallel?
Find the slope of each base.
If the slopes are the same, then it is a trapezoid.
Isosceles TrapezoidsIsosceles TrapezoidsIsosceles triangles have 2
congruent sides with 2 pairs of congruent angles.
The diagonals of an isosceles trapezoid are also congruent.
If it is Isosceles find the If it is Isosceles find the missing angles.missing angles.
It is isosceles!
Because it is an isosceles trapezoid, the base angles are congruent.Therefore m <A = m <B, and m <D = m <C
53º
Angle A and Angle D are supplementary.180 – 53 = 127
127º
127º
Find the missing angles if it Find the missing angles if it is an Isosceles Trapezoid.is an Isosceles Trapezoid.
97º
83º
83º
MidsegmentsMidsegmentsA midsegment is a segment that
connects 2 midpoints.
The midsegment of a trapezoid connects the midpoints of the legs.
Find the length of the Find the length of the midsegmentmidsegment
)(2
1GFDEHK
)186(2
1HK
12HK
Things always have to be Things always have to be more difficultmore difficult
)(2
121 basebasemigsegment
)3527(2
15.19 x
)530(2
15.19 x
x5.2155.19 x5.25.4 x8.1
19.5
5x + 3
Find xFind x)(
2
121 basebasemigsegment
)151045(2
15.52 x
)1060(2
15.52 x
x5305.52 x55.22 x5.4
52.5
45
10x + 15
Page 546, #3 – 15, 25 - 27Page 546, #3 – 15, 25 - 27
KitesKitesA kite is a quadrilateral with 2
pairs of congruent sides, but the opposite sides are not congruent.
DiagonalsDiagonals If the diagonals of a kite are perpendicular, then what shape is created by the diagonals?If we are given these side lengths, can we find the missing sides XY, WX, YZ , and WZ?
222 cba 222 33 XY299 XY
218 XY218 XY
WXXY 23
222 53 YZ2259 XY
234 XY234 XY
WZYZ 34
Find XY, ZY, WX, and WZFind XY, ZY, WX, and WZ
222 126 XY214436 XY
2180 XY2180 XYZYXY 56222 64 WX
23616 WX252 WX252 WX WZWX 132
6√52√13
Find XY, YZ, WZ, and WXFind XY, YZ, WZ, and WX222 510 XY225100 XY
2125 XY2125 XYYZXY 55
222 1910 WZ2361100 WZ
2461 WZ2461 WZWXWZ 461
5√5
√461
The figure below is a kite, The figure below is a kite, find the missing anglesfind the missing angles
What is the sum of the interior angles of a kite? 360
100 + 40 + mó E + mó G = 360 140 + mó E + mó G =
360mó E + mó G = 220What do we know about the measures of
the angles E and G?They are congruent!
1102
220
Find the missing anglesFind the missing angles
60 + 110 + 110 + mó G = 360
What do we know about the measures of the angles F and H?They are
congruent!110º
280 + mó G = 360mó G =
80
80º
Find the missing anglesFind the missing angles
150 + 90 + mó F + mó G = 360
240 + mó F + mó G = 360mó F + mó G =
120mó F = mó G
602
120