Solve for x. 30° 2x + 10 2x + 10 = 60 – 10 – 10 2x = 50 2 2 x = 25.
Warm-up 1. 5x + 4(x – 1) = 17 2. 5(x+2) = 3(x – 6) 3. 4. 5. 2x – 4(x+1) = 2x + 20.
-
Upload
myrtle-chapman -
Category
Documents
-
view
232 -
download
0
Transcript of Warm-up 1. 5x + 4(x – 1) = 17 2. 5(x+2) = 3(x – 6) 3. 4. 5. 2x – 4(x+1) = 2x + 20.
![Page 1: Warm-up 1. 5x + 4(x – 1) = 17 2. 5(x+2) = 3(x – 6) 3. 4. 5. 2x – 4(x+1) = 2x + 20.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bfcf1a28abf838ca9bed/html5/thumbnails/1.jpg)
Warm-up
1. 5x + 4(x – 1) = 172. 5(x+2) = 3(x – 6)3.
4.
5. 2x – 4(x+1) = 2x + 20
10)3(3
2x
1892
3x
![Page 2: Warm-up 1. 5x + 4(x – 1) = 17 2. 5(x+2) = 3(x – 6) 3. 4. 5. 2x – 4(x+1) = 2x + 20.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bfcf1a28abf838ca9bed/html5/thumbnails/2.jpg)
Points, Lines and PlanesSection 1.2SOL:
![Page 3: Warm-up 1. 5x + 4(x – 1) = 17 2. 5(x+2) = 3(x – 6) 3. 4. 5. 2x – 4(x+1) = 2x + 20.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bfcf1a28abf838ca9bed/html5/thumbnails/3.jpg)
PointsAn undefined term in geometry.They have no sizeHow do you represent a point?
By using a dotHow do you label a Point?
With a capital letterNever use the same letter on two
different points.What are some examples of points?
Stars, Corner of the room
A
B
BXC
![Page 4: Warm-up 1. 5x + 4(x – 1) = 17 2. 5(x+2) = 3(x – 6) 3. 4. 5. 2x – 4(x+1) = 2x + 20.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bfcf1a28abf838ca9bed/html5/thumbnails/4.jpg)
LinesUndefined term in geometry.They are made up of points and have no
thickness or width.They Extend indefinitely
There are 2 Ways to label lines:1. Using small script letter – line t2. Using any two points on the line –
Never name using three letters -
t XY
Z
zyzxyxyzxzxy ,,,,,
xyzX
![Page 5: Warm-up 1. 5x + 4(x – 1) = 17 2. 5(x+2) = 3(x – 6) 3. 4. 5. 2x – 4(x+1) = 2x + 20.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bfcf1a28abf838ca9bed/html5/thumbnails/5.jpg)
Examples of lines:Phone lines strung between poles,
spider webs, sun beams.Collinear Points:
Points that lie on the same line.
Non-collinear Points:Points that do not fall on the same line.
A
B
BA
![Page 6: Warm-up 1. 5x + 4(x – 1) = 17 2. 5(x+2) = 3(x – 6) 3. 4. 5. 2x – 4(x+1) = 2x + 20.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bfcf1a28abf838ca9bed/html5/thumbnails/6.jpg)
PlanesUndefined term in geometryAre thought of as flat surfaces that extend
indefinitely in all directions and have no thickness.
There are two ways to label planes:1. Using a capital script letter – S2. Using any three non-collinear points –
XYZ, XZY, YXZ, YZX, ZXY, ZYX
S
X
Z
Y
![Page 7: Warm-up 1. 5x + 4(x – 1) = 17 2. 5(x+2) = 3(x – 6) 3. 4. 5. 2x – 4(x+1) = 2x + 20.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bfcf1a28abf838ca9bed/html5/thumbnails/7.jpg)
Coplanar:Points that lie on the same
plane.
Non-coplanar: Points that do not lie on the
same plane.
![Page 8: Warm-up 1. 5x + 4(x – 1) = 17 2. 5(x+2) = 3(x – 6) 3. 4. 5. 2x – 4(x+1) = 2x + 20.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bfcf1a28abf838ca9bed/html5/thumbnails/8.jpg)
Example: Use the figure to name each of the following.
1. Give two other names for .2. Give two other names for Plane R.3. Name 3 collinear points.4. Name 4 points that are coplanar.5. Name a point that is not coplanar with points
Q,S,and T.
V
R
Q
SP
Tm
n
PQ
![Page 9: Warm-up 1. 5x + 4(x – 1) = 17 2. 5(x+2) = 3(x – 6) 3. 4. 5. 2x – 4(x+1) = 2x + 20.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bfcf1a28abf838ca9bed/html5/thumbnails/9.jpg)
Example: Draw and label a figure for each relationship.
RA
P
E
B
D
C
![Page 10: Warm-up 1. 5x + 4(x – 1) = 17 2. 5(x+2) = 3(x – 6) 3. 4. 5. 2x – 4(x+1) = 2x + 20.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bfcf1a28abf838ca9bed/html5/thumbnails/10.jpg)
Space
Is a boundless three dimensional set of all points. Space can contain lines and planes.
![Page 11: Warm-up 1. 5x + 4(x – 1) = 17 2. 5(x+2) = 3(x – 6) 3. 4. 5. 2x – 4(x+1) = 2x + 20.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bfcf1a28abf838ca9bed/html5/thumbnails/11.jpg)
1. How many Planes are there?2. Name three points that are
collinear.3. Are points A, B, C, & D coplanar?
Explain.4. At what point do and
intersect?
AB CD
![Page 12: Warm-up 1. 5x + 4(x – 1) = 17 2. 5(x+2) = 3(x – 6) 3. 4. 5. 2x – 4(x+1) = 2x + 20.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bfcf1a28abf838ca9bed/html5/thumbnails/12.jpg)
1. How any planes are there?2. Name three collinear points.3. Are points G, A, B, & F coplanar?
Explain4. At what point do and
intersect?
EF AB
![Page 13: Warm-up 1. 5x + 4(x – 1) = 17 2. 5(x+2) = 3(x – 6) 3. 4. 5. 2x – 4(x+1) = 2x + 20.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bfcf1a28abf838ca9bed/html5/thumbnails/13.jpg)
Activity1. Each student gets two cards2. Label one Q and one R.3. Hold the two card together and place
a slit halfway through both cards.4. Hold cards so that the slits matchup
and slide them together. (Tape cards together)
5. Where the cards meet models a line. Draw the line and label two points C and D on the line.
![Page 14: Warm-up 1. 5x + 4(x – 1) = 17 2. 5(x+2) = 3(x – 6) 3. 4. 5. 2x – 4(x+1) = 2x + 20.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bfcf1a28abf838ca9bed/html5/thumbnails/14.jpg)
Activity Cont.
1. Draw point F on your model so that it lies in Q but not R. Can F lie on line DC?
2. Draw point G so that is lies in R but not Q. Can G lie on line DC?
3. If point H lies in both Q and R where would it lie? Draw it on your model.
4. Draw a sketch of your model on your paper. Label each thing appropriately.
![Page 15: Warm-up 1. 5x + 4(x – 1) = 17 2. 5(x+2) = 3(x – 6) 3. 4. 5. 2x – 4(x+1) = 2x + 20.](https://reader035.fdocuments.net/reader035/viewer/2022062217/5697bfcf1a28abf838ca9bed/html5/thumbnails/15.jpg)
Assignments
Classwork: WB PG 7 1-17, 20, 21, 23, 27
Homework - Handouts