geometry 4
DESCRIPTION
Geometry 4. Level 1. Are the lines parallel?. Corresponding Angles are equal. Corresponding angles. a. a. Vertically opposite angles are equal. a. a. a. Alternate angles are equal. a. a. a. Are these lines parallel?. a + c = 180 ( ). a + c = 180 ( ). - PowerPoint PPT PresentationTRANSCRIPT
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Geometry 4
Level 1
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Are the lines parallel?
![Page 3: Geometry 4](https://reader035.vdocuments.net/reader035/viewer/2022062315/568159c4550346895dc715f3/html5/thumbnails/3.jpg)
![Page 4: Geometry 4](https://reader035.vdocuments.net/reader035/viewer/2022062315/568159c4550346895dc715f3/html5/thumbnails/4.jpg)
![Page 5: Geometry 4](https://reader035.vdocuments.net/reader035/viewer/2022062315/568159c4550346895dc715f3/html5/thumbnails/5.jpg)
![Page 6: Geometry 4](https://reader035.vdocuments.net/reader035/viewer/2022062315/568159c4550346895dc715f3/html5/thumbnails/6.jpg)
CorrespondingAngles are equal
![Page 7: Geometry 4](https://reader035.vdocuments.net/reader035/viewer/2022062315/568159c4550346895dc715f3/html5/thumbnails/7.jpg)
Corresponding angles
a
a
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.Corr∠' // s lines
![Page 8: Geometry 4](https://reader035.vdocuments.net/reader035/viewer/2022062315/568159c4550346895dc715f3/html5/thumbnails/8.jpg)
Vertically opposite angles are equal
a
a
a
![Page 9: Geometry 4](https://reader035.vdocuments.net/reader035/viewer/2022062315/568159c4550346895dc715f3/html5/thumbnails/9.jpg)
Alternate angles are equal
a
a
a
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. alt∠' // s lines
![Page 10: Geometry 4](https://reader035.vdocuments.net/reader035/viewer/2022062315/568159c4550346895dc715f3/html5/thumbnails/10.jpg)
Are these lines parallel?
![Page 11: Geometry 4](https://reader035.vdocuments.net/reader035/viewer/2022062315/568159c4550346895dc715f3/html5/thumbnails/11.jpg)
a + c = 180 ( )
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∠' s on line
![Page 12: Geometry 4](https://reader035.vdocuments.net/reader035/viewer/2022062315/568159c4550346895dc715f3/html5/thumbnails/12.jpg)
a + c = 180 ( )
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∠' s on line
These must addto 180
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a + c = 180 (co-interior angles)
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. coint∠' // s lines
![Page 14: Geometry 4](https://reader035.vdocuments.net/reader035/viewer/2022062315/568159c4550346895dc715f3/html5/thumbnails/14.jpg)
Are these lines parallel?
![Page 15: Geometry 4](https://reader035.vdocuments.net/reader035/viewer/2022062315/568159c4550346895dc715f3/html5/thumbnails/15.jpg)
a
a
a
a
a
b
€
. corr∠' // s lines
€
. alt∠' // s lines
€
. coint∠’ // s lines
![Page 16: Geometry 4](https://reader035.vdocuments.net/reader035/viewer/2022062315/568159c4550346895dc715f3/html5/thumbnails/16.jpg)
a
a
b
b
c
c
€
. corr∠' // s lines
€
. corr∠' // s lines
€
. corr∠' // s lines
![Page 17: Geometry 4](https://reader035.vdocuments.net/reader035/viewer/2022062315/568159c4550346895dc715f3/html5/thumbnails/17.jpg)
aa
b
b
€
. alt∠' // s lines
€
. alt∠' // s lines
![Page 18: Geometry 4](https://reader035.vdocuments.net/reader035/viewer/2022062315/568159c4550346895dc715f3/html5/thumbnails/18.jpg)
a
b
a
b
€
. coint∠' // s lines
€
. coint∠’ // s lines
![Page 19: Geometry 4](https://reader035.vdocuments.net/reader035/viewer/2022062315/568159c4550346895dc715f3/html5/thumbnails/19.jpg)
Match the corresponding angles
![Page 20: Geometry 4](https://reader035.vdocuments.net/reader035/viewer/2022062315/568159c4550346895dc715f3/html5/thumbnails/20.jpg)
Match the corresponding angles
![Page 21: Geometry 4](https://reader035.vdocuments.net/reader035/viewer/2022062315/568159c4550346895dc715f3/html5/thumbnails/21.jpg)
Match the corresponding angles
![Page 22: Geometry 4](https://reader035.vdocuments.net/reader035/viewer/2022062315/568159c4550346895dc715f3/html5/thumbnails/22.jpg)
Match the corresponding angles
![Page 23: Geometry 4](https://reader035.vdocuments.net/reader035/viewer/2022062315/568159c4550346895dc715f3/html5/thumbnails/23.jpg)
Match the corresponding angles
![Page 24: Geometry 4](https://reader035.vdocuments.net/reader035/viewer/2022062315/568159c4550346895dc715f3/html5/thumbnails/24.jpg)
Match the alternate angles
![Page 25: Geometry 4](https://reader035.vdocuments.net/reader035/viewer/2022062315/568159c4550346895dc715f3/html5/thumbnails/25.jpg)
Match the alternate angles
![Page 26: Geometry 4](https://reader035.vdocuments.net/reader035/viewer/2022062315/568159c4550346895dc715f3/html5/thumbnails/26.jpg)
Match the alternate angles
![Page 27: Geometry 4](https://reader035.vdocuments.net/reader035/viewer/2022062315/568159c4550346895dc715f3/html5/thumbnails/27.jpg)
Match the co-interior angles
![Page 28: Geometry 4](https://reader035.vdocuments.net/reader035/viewer/2022062315/568159c4550346895dc715f3/html5/thumbnails/28.jpg)
Match the co-interior angles
![Page 29: Geometry 4](https://reader035.vdocuments.net/reader035/viewer/2022062315/568159c4550346895dc715f3/html5/thumbnails/29.jpg)
Match the co-interior angles
![Page 30: Geometry 4](https://reader035.vdocuments.net/reader035/viewer/2022062315/568159c4550346895dc715f3/html5/thumbnails/30.jpg)
Are the lines parallel?
![Page 31: Geometry 4](https://reader035.vdocuments.net/reader035/viewer/2022062315/568159c4550346895dc715f3/html5/thumbnails/31.jpg)
Find all the angles
€
120°
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Find all the angles
€
120°
€
120°
€
120°
€
120°
€
60°
€
60°
€
60°
€
60°
![Page 33: Geometry 4](https://reader035.vdocuments.net/reader035/viewer/2022062315/568159c4550346895dc715f3/html5/thumbnails/33.jpg)
Find value of x and give the reason
€
50°
€
x
![Page 34: Geometry 4](https://reader035.vdocuments.net/reader035/viewer/2022062315/568159c4550346895dc715f3/html5/thumbnails/34.jpg)
€
50°
€
50°
€
. corr∠' // s lines
![Page 35: Geometry 4](https://reader035.vdocuments.net/reader035/viewer/2022062315/568159c4550346895dc715f3/html5/thumbnails/35.jpg)
Find value of x and give the reason
€
130°
€
x
![Page 36: Geometry 4](https://reader035.vdocuments.net/reader035/viewer/2022062315/568159c4550346895dc715f3/html5/thumbnails/36.jpg)
€
130°
€
130°
€
. corr∠' // s lines
![Page 37: Geometry 4](https://reader035.vdocuments.net/reader035/viewer/2022062315/568159c4550346895dc715f3/html5/thumbnails/37.jpg)
Find value of x and give the reason
€
110°
€
x
![Page 38: Geometry 4](https://reader035.vdocuments.net/reader035/viewer/2022062315/568159c4550346895dc715f3/html5/thumbnails/38.jpg)
€
110°
€
110°
€
. alt∠' // s lines
![Page 39: Geometry 4](https://reader035.vdocuments.net/reader035/viewer/2022062315/568159c4550346895dc715f3/html5/thumbnails/39.jpg)
Find value of x and give the reason
€
55°
€
x
![Page 40: Geometry 4](https://reader035.vdocuments.net/reader035/viewer/2022062315/568159c4550346895dc715f3/html5/thumbnails/40.jpg)
€
55°
€
55°
€
. alt∠' // s lines
![Page 41: Geometry 4](https://reader035.vdocuments.net/reader035/viewer/2022062315/568159c4550346895dc715f3/html5/thumbnails/41.jpg)
Find value of x and give the reason
€
55°
€
x
![Page 42: Geometry 4](https://reader035.vdocuments.net/reader035/viewer/2022062315/568159c4550346895dc715f3/html5/thumbnails/42.jpg)
€
55°
€
125°
€
. coint∠' // s lines
![Page 43: Geometry 4](https://reader035.vdocuments.net/reader035/viewer/2022062315/568159c4550346895dc715f3/html5/thumbnails/43.jpg)
Find x, y, w, u and v and give reasons for your answers.
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x = 40, coint ∠’s // lines
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y = 20, coint ∠’s // lines
![Page 46: Geometry 4](https://reader035.vdocuments.net/reader035/viewer/2022062315/568159c4550346895dc715f3/html5/thumbnails/46.jpg)
w = 40, alt ∠’s // lines
![Page 47: Geometry 4](https://reader035.vdocuments.net/reader035/viewer/2022062315/568159c4550346895dc715f3/html5/thumbnails/47.jpg)
u = 140, coint ∠’s // lines
![Page 48: Geometry 4](https://reader035.vdocuments.net/reader035/viewer/2022062315/568159c4550346895dc715f3/html5/thumbnails/48.jpg)
u = 28, vert opp. ∠’s
![Page 49: Geometry 4](https://reader035.vdocuments.net/reader035/viewer/2022062315/568159c4550346895dc715f3/html5/thumbnails/49.jpg)
Find the value of y
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Corr. ∠’s // lines
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5y−5=90
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Corr. ∠’s // lines
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5y−5=90y=19°
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Find the values of x and y. Give reasons.
![Page 53: Geometry 4](https://reader035.vdocuments.net/reader035/viewer/2022062315/568159c4550346895dc715f3/html5/thumbnails/53.jpg)
Find the values of x and y. Give reasons.
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6x+14 =9x−10 Corr. ∠’s // lines
Take 6x from each side
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Find the values of x and y. Give reasons.
€
14 =3x−10 Work backwards
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Find the values of x and y. Give reasons.
€
24 =3x8 =x
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Find the values of x and y. Give reasons.
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2y−2=9x−10 Vert. opp. ∠’s
€
x=8
€
⇒ 2y−2=62
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Find the values of x and y. Give reasons.
€
2y−2=9x−10
€
⇒ 2y−2=62 ⇒ 2y=64 ⇒ y=32°
![Page 58: Geometry 4](https://reader035.vdocuments.net/reader035/viewer/2022062315/568159c4550346895dc715f3/html5/thumbnails/58.jpg)
Why is AB is parallel to CD?
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Find x
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If AD is parallel to BC, and AC = CE, find all the other angles.
60
70
![Page 61: Geometry 4](https://reader035.vdocuments.net/reader035/viewer/2022062315/568159c4550346895dc715f3/html5/thumbnails/61.jpg)
Were you right?
60
70
6070
25 25859595
50
110
![Page 62: Geometry 4](https://reader035.vdocuments.net/reader035/viewer/2022062315/568159c4550346895dc715f3/html5/thumbnails/62.jpg)
Find x and y
![Page 63: Geometry 4](https://reader035.vdocuments.net/reader035/viewer/2022062315/568159c4550346895dc715f3/html5/thumbnails/63.jpg)
APR = RPQ = 20,
CQR = RQP, find ∠PRQ
![Page 64: Geometry 4](https://reader035.vdocuments.net/reader035/viewer/2022062315/568159c4550346895dc715f3/html5/thumbnails/64.jpg)
APR = RPQ = 20,
CQR = RQP, find ∠PRQ
€
90°
![Page 65: Geometry 4](https://reader035.vdocuments.net/reader035/viewer/2022062315/568159c4550346895dc715f3/html5/thumbnails/65.jpg)
Find all the angles.
130
![Page 66: Geometry 4](https://reader035.vdocuments.net/reader035/viewer/2022062315/568159c4550346895dc715f3/html5/thumbnails/66.jpg)
Find all the angles.
130
130
![Page 67: Geometry 4](https://reader035.vdocuments.net/reader035/viewer/2022062315/568159c4550346895dc715f3/html5/thumbnails/67.jpg)
Find all the angles.
130
130
50
![Page 68: Geometry 4](https://reader035.vdocuments.net/reader035/viewer/2022062315/568159c4550346895dc715f3/html5/thumbnails/68.jpg)
Find all the angles.
130
130
50
50
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Find all the angles.
130
130
50
5040
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Find all the angles.
130
130
50
5040
40
![Page 71: Geometry 4](https://reader035.vdocuments.net/reader035/viewer/2022062315/568159c4550346895dc715f3/html5/thumbnails/71.jpg)
Find all the angles.
130
130
50
5040
40 140
140
![Page 72: Geometry 4](https://reader035.vdocuments.net/reader035/viewer/2022062315/568159c4550346895dc715f3/html5/thumbnails/72.jpg)
Find as many angles as you can