Use Properties of Trapezoids and Kites
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Transcript of Use Properties of Trapezoids and Kites
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Use Properties of Use Properties of Trapezoids and KitesTrapezoids and KitesChapter 8.5
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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
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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.
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Isosceles TrapezoidsIsosceles TrapezoidsIsosceles triangles have 2
congruent sides with 2 pairs of congruent angles.
The diagonals of an isosceles trapezoid are also congruent.
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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
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Find the missing angles if it Find the missing angles if it is an Isosceles Trapezoid.is an Isosceles Trapezoid.
97º
83º
83º
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MidsegmentsMidsegmentsA midsegment is a segment that
connects 2 midpoints.
The midsegment of a trapezoid connects the midpoints of the legs.
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Find the length of the Find the length of the midsegmentmidsegment
)(2
1GFDEHK
)186(2
1HK
12HK
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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
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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
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Page 546, #3 – 15, 25 - 27Page 546, #3 – 15, 25 - 27
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KitesKitesA kite is a quadrilateral with 2
pairs of congruent sides, but the opposite sides are not congruent.
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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
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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
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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
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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
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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
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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