Honors Geometry Section 4.5 (3) Trapezoids and Kites.
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Transcript of Honors Geometry Section 4.5 (3) Trapezoids and Kites.
![Page 1: Honors Geometry Section 4.5 (3) Trapezoids and Kites.](https://reader036.fdocuments.us/reader036/viewer/2022082709/56649d8b5503460f94a71a2a/html5/thumbnails/1.jpg)
Honors Geometry Section 4.5 (3)
Trapezoids and Kites
![Page 2: Honors Geometry Section 4.5 (3) Trapezoids and Kites.](https://reader036.fdocuments.us/reader036/viewer/2022082709/56649d8b5503460f94a71a2a/html5/thumbnails/2.jpg)
Two special types of quadrilaterals that are NOT parallelograms are
trapezoids and kites.
![Page 3: Honors Geometry Section 4.5 (3) Trapezoids and Kites.](https://reader036.fdocuments.us/reader036/viewer/2022082709/56649d8b5503460f94a71a2a/html5/thumbnails/3.jpg)
A trapezoid is a quadrilateral with exactly one pair of opposite sides parallel.
The sides that are parallel are called _______.
The nonparallel sides are called ______.
The angles at each end of a base are called _____________.
bases
legs
base angles
![Page 4: Honors Geometry Section 4.5 (3) Trapezoids and Kites.](https://reader036.fdocuments.us/reader036/viewer/2022082709/56649d8b5503460f94a71a2a/html5/thumbnails/4.jpg)
A midsegment of a trapezoid is the segment joining the midpoints of
the two legs.
![Page 5: Honors Geometry Section 4.5 (3) Trapezoids and Kites.](https://reader036.fdocuments.us/reader036/viewer/2022082709/56649d8b5503460f94a71a2a/html5/thumbnails/5.jpg)
Theorem The midsegment of a trapezoid is parallel
to the bases and the length of the midsegment is equal to ½ the sum of the
bases.
FCEDAB ////
EDABFC
EDABFC
221
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An isosceles trapezoid is a trapezoid that has congruent legs.
![Page 7: Honors Geometry Section 4.5 (3) Trapezoids and Kites.](https://reader036.fdocuments.us/reader036/viewer/2022082709/56649d8b5503460f94a71a2a/html5/thumbnails/7.jpg)
Theorem In an isosceles trapezoid, the base angles that share a common base are congruent.
Note: For any trapezoid the angles that share a common leg are _____________.supplementary
![Page 8: Honors Geometry Section 4.5 (3) Trapezoids and Kites.](https://reader036.fdocuments.us/reader036/viewer/2022082709/56649d8b5503460f94a71a2a/html5/thumbnails/8.jpg)
Theorem
The diagonals of an isosceles trapezoid are congruent.
![Page 9: Honors Geometry Section 4.5 (3) Trapezoids and Kites.](https://reader036.fdocuments.us/reader036/viewer/2022082709/56649d8b5503460f94a71a2a/html5/thumbnails/9.jpg)
Example 1: Find the value of x, y and z in this isosceles trapezoid.
43y
137z
25.16885
8568
47123880
318164)1940(2
x
x
xx
xxx
![Page 10: Honors Geometry Section 4.5 (3) Trapezoids and Kites.](https://reader036.fdocuments.us/reader036/viewer/2022082709/56649d8b5503460f94a71a2a/html5/thumbnails/10.jpg)
A kite is a quadrilateral with two pairs of congruent adjacent sides and noncongruent opposite sides.
![Page 11: Honors Geometry Section 4.5 (3) Trapezoids and Kites.](https://reader036.fdocuments.us/reader036/viewer/2022082709/56649d8b5503460f94a71a2a/html5/thumbnails/11.jpg)
Theorem
The diagonals of a kite are perpendicular.
![Page 12: Honors Geometry Section 4.5 (3) Trapezoids and Kites.](https://reader036.fdocuments.us/reader036/viewer/2022082709/56649d8b5503460f94a71a2a/html5/thumbnails/12.jpg)
Example 2: Find the perimeter of the kite.
222 5.1318 c5.22c
222 4.325.13 c1.35c
2.115)1.35(2)5.22(2 P