3B ­ Lesson 6 ­ Prisms and Cylinders.notebook
On p 179 (S.33)
Sketch a right rectangular prism
March 24, 2017
Need Sc
3B ­ Lesson 6 ­ Prisms and Cylinders.notebook
March 24, 2017
p 177
A
N
S
A
N
S
S
S
p 177
Perpendicular to // planes
Yes
No
Yes
No
3B ­ Lesson 6 ­ Prisms and Cylinders.notebook
On p 179
Sketch a right rectangular prism
Today we formalize and extend our definition of prisms
March 24, 2017
3B ­ Lesson 6 ­ Prisms and Cylinders.notebook
March 24, 2017
p 177
So what does this mean? if you want to draw along, do it on the top of 177
We break it down into 4 steps
Now what?
show with pasta?
While we don't normally draw prisms this way, this definition tells us why these are solids (not hollow)
3B ­ Lesson 6 ­ Prisms and Cylinders.notebook
March 24, 2017
We now generalize our definition of a right rectangular prism to a general cylinder. p 177
Compare our two definitions
How are they different?
­Region we start with.
­Angle at which the segments intersect the planes
When our segments are perpendicular to the base planes, we have a right cylinder
When our segments are not perpendicular to the base planes, we have an oblique cylinder
3B ­ Lesson 6 ­ Prisms and Cylinders.notebook
March 24, 2017
We are now going to sort different solids.
on p 182, there are 6 pictures. You are going to cut them out (the boxes their in are fine) and then arrange where you think they belong in the diagram on p 180.
Once we agree where they go, you will tape/
glue/staple them to the chart.
3B ­ Lesson 6 ­ Prisms and Cylinders.notebook
March 24, 2017
3B ­ Lesson 6 ­ Prisms and Cylinders.notebook
March 24, 2017
p 184
3B ­ Lesson 6 ­ Prisms and Cylinders.notebook
March 24, 2017
Just like yesterday with the Pythagorean p 185
theorem example, we want to be able to take 2 dimensional components of the solids.
cross sections ­ the 2 ­ D shape we get when we cut a solid parallel to the base
If we don't use a plane parallel to the base, the intersection is called a slice.
animation
3B ­ Lesson 6 ­ Prisms and Cylinders.notebook
March 24, 2017
p 185
Classify the solids
3B ­ Lesson 6 ­ Prisms and Cylinders.notebook
March 24, 2017
p 186
What can we say about all of the cross sections for a general cylinder?
They are congruent !!
We are essentially doing a translation in 3 dimensions
proof
AX // BX // L­ def of cylinder
XY//AB ­ in parallel planes (need for CS)
AXYB is parallelogram ­ def
AB = AX ­ opp sides of parallelogram
Likewise for each side
ΔABC≅ΔXYZ ­ SSS
So there is a sequence of rigid motions (1 translation) that map them
This is a key idea when we talk about volume
3B ­ Lesson 6 ­ Prisms and Cylinders.notebook
Assignment: p 187 # 7
p 188 # 2
exit: p 188 #1
March 24, 2017