Polygons – Rhombuses and Trapezoids Rhombus - four congruent sides.
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Transcript of Polygons – Rhombuses and Trapezoids Rhombus - four congruent sides.
![Page 1: Polygons – Rhombuses and Trapezoids Rhombus - four congruent sides.](https://reader035.fdocuments.net/reader035/viewer/2022062422/56649ea05503460f94ba398c/html5/thumbnails/1.jpg)
Polygons – Rhombuses and Trapezoids
Rhombus - four congruent sides
![Page 2: Polygons – Rhombuses and Trapezoids Rhombus - four congruent sides.](https://reader035.fdocuments.net/reader035/viewer/2022062422/56649ea05503460f94ba398c/html5/thumbnails/2.jpg)
Polygons – Rhombuses and Trapezoids
Rhombus - four congruent sides
- opposite angles are congruent
![Page 3: Polygons – Rhombuses and Trapezoids Rhombus - four congruent sides.](https://reader035.fdocuments.net/reader035/viewer/2022062422/56649ea05503460f94ba398c/html5/thumbnails/3.jpg)
Polygons – Rhombuses and Trapezoids
Rhombus - four congruent sides
- opposite angles are congruent
![Page 4: Polygons – Rhombuses and Trapezoids Rhombus - four congruent sides.](https://reader035.fdocuments.net/reader035/viewer/2022062422/56649ea05503460f94ba398c/html5/thumbnails/4.jpg)
Polygons – Rhombuses and Trapezoids
Rhombus - four congruent sides
- opposite angles are congruent
- diagonals bisect the angles at the vertex
A
C
B
D
2
2A
CAD
ACAB
![Page 5: Polygons – Rhombuses and Trapezoids Rhombus - four congruent sides.](https://reader035.fdocuments.net/reader035/viewer/2022062422/56649ea05503460f94ba398c/html5/thumbnails/5.jpg)
Polygons – Rhombuses and Trapezoids
Rhombus - four congruent sides
- opposite angles are congruent
- diagonals bisect the angles at the vertex
- diagonals bisect each other and are perpendicular
A
C
B
D
E ACBD
ECAE
EDBE
![Page 6: Polygons – Rhombuses and Trapezoids Rhombus - four congruent sides.](https://reader035.fdocuments.net/reader035/viewer/2022062422/56649ea05503460f94ba398c/html5/thumbnails/6.jpg)
Polygons – Rhombuses and Trapezoids
Rhombus - four congruent sides
- opposite angles are congruent
- diagonals bisect the angles at the vertex
- diagonals bisect each other and are perpendicular
A
C
B
D
E14
EXAMPLE : If AD = 14, what is the measure of EB ?
60°
![Page 7: Polygons – Rhombuses and Trapezoids Rhombus - four congruent sides.](https://reader035.fdocuments.net/reader035/viewer/2022062422/56649ea05503460f94ba398c/html5/thumbnails/7.jpg)
Polygons – Rhombuses and Trapezoids
Rhombus - four congruent sides
- opposite angles are congruent
- diagonals bisect the angles at the vertex
- diagonals bisect each other and are perpendicular
A
C
B
D
E14
EXAMPLE : If AD = 14, what is the measure of EB ?
SOLUTION : With angle ADE = 60 degrees we have a 30 – 60 – 90 triangle.
So segment EB = Segment ED which is half of AD.
60°
![Page 8: Polygons – Rhombuses and Trapezoids Rhombus - four congruent sides.](https://reader035.fdocuments.net/reader035/viewer/2022062422/56649ea05503460f94ba398c/html5/thumbnails/8.jpg)
Polygons – Rhombuses and Trapezoids
Rhombus - four congruent sides
- opposite angles are congruent
- diagonals bisect the angles at the vertex
- diagonals bisect each other and are perpendicular
A
C
B
D
E14
EXAMPLE : If AD = 14, what is the measure of EB ?
SOLUTION : With angle ADE = 60 degrees we have a 30 – 60 – 90 triangle.
So segment EB = Segment ED which is half of AD. ED = 7
60°
![Page 9: Polygons – Rhombuses and Trapezoids Rhombus - four congruent sides.](https://reader035.fdocuments.net/reader035/viewer/2022062422/56649ea05503460f94ba398c/html5/thumbnails/9.jpg)
Polygons – Rhombuses and Trapezoids
Rhombus - four congruent sides
- opposite angles are congruent
- diagonals bisect the angles at the vertex
- diagonals bisect each other and are perpendicular
A
C
B
D
E14
EXAMPLE : What is the measure of angle ECD ?
60°
![Page 10: Polygons – Rhombuses and Trapezoids Rhombus - four congruent sides.](https://reader035.fdocuments.net/reader035/viewer/2022062422/56649ea05503460f94ba398c/html5/thumbnails/10.jpg)
Polygons – Rhombuses and Trapezoids
Rhombus - four congruent sides
- opposite angles are congruent
- diagonals bisect the angles at the vertex
- diagonals bisect each other and are perpendicular
A
C
B
D
E14
EXAMPLE : What is the measure of angle ECD ?
SOLUTION : Again we have a 30 – 60 – 90 triangle. So angle DAC = 30 degrees.
60°
![Page 11: Polygons – Rhombuses and Trapezoids Rhombus - four congruent sides.](https://reader035.fdocuments.net/reader035/viewer/2022062422/56649ea05503460f94ba398c/html5/thumbnails/11.jpg)
Polygons – Rhombuses and Trapezoids
Rhombus - four congruent sides
- opposite angles are congruent
- diagonals bisect the angles at the vertex
- diagonals bisect each other and are perpendicular
A
C
B
D
E14
EXAMPLE : What is the measure of angle ECD ?
SOLUTION : Again we have a 30 – 60 – 90 triangle. So angle DAC = 30 degrees.
So angle ECD would also be 30 degrees.
60°
![Page 12: Polygons – Rhombuses and Trapezoids Rhombus - four congruent sides.](https://reader035.fdocuments.net/reader035/viewer/2022062422/56649ea05503460f94ba398c/html5/thumbnails/12.jpg)
Polygons – Rhombuses and Trapezoids
Trapezoid - two parallel sides that are not congruent
D
A B
C
CDAB ║
CDAB
![Page 13: Polygons – Rhombuses and Trapezoids Rhombus - four congruent sides.](https://reader035.fdocuments.net/reader035/viewer/2022062422/56649ea05503460f94ba398c/html5/thumbnails/13.jpg)
Polygons – Rhombuses and Trapezoids
Trapezoid - two parallel sides that are not congruent
D
A B
C
CDAB ║
CDAB - these parallel sides are called bases
- non-parallel sides are called legs
base 1
base 2
leg leg
![Page 14: Polygons – Rhombuses and Trapezoids Rhombus - four congruent sides.](https://reader035.fdocuments.net/reader035/viewer/2022062422/56649ea05503460f94ba398c/html5/thumbnails/14.jpg)
Polygons – Rhombuses and Trapezoids
Trapezoid - two parallel sides that are not congruent
D
A B
C
CDAB ║
CDAB - these parallel sides are called bases
- non-parallel sides are called legs
base 1
base 2
leg leg
- there are two pairs of base angles
![Page 15: Polygons – Rhombuses and Trapezoids Rhombus - four congruent sides.](https://reader035.fdocuments.net/reader035/viewer/2022062422/56649ea05503460f94ba398c/html5/thumbnails/15.jpg)
Polygons – Rhombuses and Trapezoids
Trapezoid - two parallel sides that are not congruent
D
A B
C
CDAB ║
CDAB - these parallel sides are called bases
- non-parallel sides are called legs
base 1
base 2
leg leg
- there are two pairs of base angles
- diagonal base angles are supplementary
![Page 16: Polygons – Rhombuses and Trapezoids Rhombus - four congruent sides.](https://reader035.fdocuments.net/reader035/viewer/2022062422/56649ea05503460f94ba398c/html5/thumbnails/16.jpg)
Polygons – Rhombuses and Trapezoids
Trapezoid - two parallel sides that are not congruent
D
A B
C
CDAB ║
CDAB - these parallel sides are called bases
- non-parallel sides are called legs
base 1
base 2
leg leg
- there are two pairs of base angles
- diagonal base angles are supplementary
- base angles that share a leg are also supplementary
![Page 17: Polygons – Rhombuses and Trapezoids Rhombus - four congruent sides.](https://reader035.fdocuments.net/reader035/viewer/2022062422/56649ea05503460f94ba398c/html5/thumbnails/17.jpg)
Polygons – Rhombuses and Trapezoids
Isosceles Trapezoid - has all the properties of a trapezoid
- legs are congruent
- base angles are congruent
D
A B
C
DC
BA
![Page 18: Polygons – Rhombuses and Trapezoids Rhombus - four congruent sides.](https://reader035.fdocuments.net/reader035/viewer/2022062422/56649ea05503460f94ba398c/html5/thumbnails/18.jpg)
Polygons – Rhombuses and Trapezoids
Isosceles Trapezoid - has all the properties of a trapezoid
- legs are congruent
- base angles are congruent
- diagonals have the same length
D
A B
C
DC
BA
BDAC
![Page 19: Polygons – Rhombuses and Trapezoids Rhombus - four congruent sides.](https://reader035.fdocuments.net/reader035/viewer/2022062422/56649ea05503460f94ba398c/html5/thumbnails/19.jpg)
Polygons – Rhombuses and Trapezoids
Median of a Trapezoid
- parallel with both bases
- equal to half the sum of the bases
- joins the midpoints of the legs
D
A B
C
2
21 basebase
X Y
![Page 20: Polygons – Rhombuses and Trapezoids Rhombus - four congruent sides.](https://reader035.fdocuments.net/reader035/viewer/2022062422/56649ea05503460f94ba398c/html5/thumbnails/20.jpg)
Polygons – Rhombuses and Trapezoids
Let’s try some problems…
D
A B
C
EXAMPLE : What is the median length ?
20
28
![Page 21: Polygons – Rhombuses and Trapezoids Rhombus - four congruent sides.](https://reader035.fdocuments.net/reader035/viewer/2022062422/56649ea05503460f94ba398c/html5/thumbnails/21.jpg)
Polygons – Rhombuses and Trapezoids
Let’s try some problems…
D
A B
C
EXAMPLE : What is the median length ?
20
28
242
48
2
2820
2
21
basebase
24
![Page 22: Polygons – Rhombuses and Trapezoids Rhombus - four congruent sides.](https://reader035.fdocuments.net/reader035/viewer/2022062422/56649ea05503460f94ba398c/html5/thumbnails/22.jpg)
Polygons – Rhombuses and Trapezoids
Let’s try some problems…
D
A B
C
EXAMPLE : If AD = 18, what is the measure of AX ?
18 X Y
![Page 23: Polygons – Rhombuses and Trapezoids Rhombus - four congruent sides.](https://reader035.fdocuments.net/reader035/viewer/2022062422/56649ea05503460f94ba398c/html5/thumbnails/23.jpg)
Polygons – Rhombuses and Trapezoids
Let’s try some problems…
D
A B
C
EXAMPLE : If AD = 18, what is the measure of AX ?
18 X Y
92
18 The median joins the midpoints of the legs
![Page 24: Polygons – Rhombuses and Trapezoids Rhombus - four congruent sides.](https://reader035.fdocuments.net/reader035/viewer/2022062422/56649ea05503460f94ba398c/html5/thumbnails/24.jpg)
Polygons – Rhombuses and Trapezoids
Let’s try some problems…
D
A B
C
EXAMPLE : ABCD is an isosceles trapezoid. If angle DAB = 110°, what is the measure of angle ABC ?
![Page 25: Polygons – Rhombuses and Trapezoids Rhombus - four congruent sides.](https://reader035.fdocuments.net/reader035/viewer/2022062422/56649ea05503460f94ba398c/html5/thumbnails/25.jpg)
Polygons – Rhombuses and Trapezoids
Let’s try some problems…
D
A B
C
EXAMPLE : ABCD is an isosceles trapezoid. If angle DAB = 110°, what is the measure of angle ABC ?
110° - base angles are congruent in an isosceles trapezoid
![Page 26: Polygons – Rhombuses and Trapezoids Rhombus - four congruent sides.](https://reader035.fdocuments.net/reader035/viewer/2022062422/56649ea05503460f94ba398c/html5/thumbnails/26.jpg)
Polygons – Rhombuses and Trapezoids
Let’s try some problems…
D
A B
C
EXAMPLE : What is the length of side AB?
?
50
YX 40
![Page 27: Polygons – Rhombuses and Trapezoids Rhombus - four congruent sides.](https://reader035.fdocuments.net/reader035/viewer/2022062422/56649ea05503460f94ba398c/html5/thumbnails/27.jpg)
Polygons – Rhombuses and Trapezoids
Let’s try some problems…
D
A B
C
EXAMPLE : What is the length of side AB?
?
50
YX 40
2
25040
base
![Page 28: Polygons – Rhombuses and Trapezoids Rhombus - four congruent sides.](https://reader035.fdocuments.net/reader035/viewer/2022062422/56649ea05503460f94ba398c/html5/thumbnails/28.jpg)
Polygons – Rhombuses and Trapezoids
Let’s try some problems…
D
A B
C
EXAMPLE : What is the length of side AB?
?
50
YX 40
22
250240
base2
25040
base
![Page 29: Polygons – Rhombuses and Trapezoids Rhombus - four congruent sides.](https://reader035.fdocuments.net/reader035/viewer/2022062422/56649ea05503460f94ba398c/html5/thumbnails/29.jpg)
Polygons – Rhombuses and Trapezoids
Let’s try some problems…
D
A B
C
EXAMPLE : What is the length of side AB?
?
50
YX 40
230
25080
22
250240
base
base
base
2
25040
base