Warm-upSIMILARITY,

cont’d

New Topics:SOLIDSPRISMSCYLINDERS

Agenda for today

Lighthouse – how tall is the real thing if the scale of this model is 1:1200?

Elephant – how tall is the real thing if the scale of this model is 1:120?

Car – come up with the scale based on the actual length of Dodge’s 2005 Charger: 200 inches

Ship’s cannon – come up with the scale based on an actual barrel length of 5 feet

Beaver – If the actual length of Castor canadensis is 2 feet from snout to tip of tail and model length is 2 inches, what is the scale?

Quarters – when the case is open, what is the ratio of area of paper to area of quarters?

Eyeballs – if real human eyes are 1 inch in diameter, what is the scale of the chocolate eyeball model?

Green plastic design tool – draw (and furnish) a room and label the scale factor

Bicycle map – based on the map’s scale, what is the closest that the Willamette River gets to Rocky Butte (as the paper airplane flies)

More…

Triangles are similar if they…

Have the same angle sizes in the same order (AA)

Have corresponding sides whose ratios are equal (SSS)

Have two corresponding sides with the same angle between them (SAS)

FIRST PROBLEM SET

Similar polygons (con't)

Draw similar polygons

Create a scale drawing

Determine whether two polygons are similar or not

SECOND PROBLEM SET

Similar polygonsTASKS

What is the relationship between the size of individual triangles’ interior angles and the sides across from them?

Discussion question

Are 3-dimensional

Some have only polygons for faces and are called polyhedra (singular, polyhedron)

Topic: Solids

Solids (continued)This one is a polyhedron:

Solids (continued)This one is not a polyhedron: LINK

Include prisms, pyramids, cylinders, cones, and spheres

Have surface area (units are squared)

Have volume (units are cubed)

Solids (continued)

Examples of different types:

Solids (continued)

Surface area is like…

Volume is like…

Use a formula to find the surface area

Use a formula to find the volume

Correctly label with specific terms

THIRD PROBLEM SET

Solids TASKS

Have 2 identical (congruent) faces (called bases – these lie in parallel planes)

Solids: Prisms

Are named for the shape of their bases

pentagonal prism vs. hexagonal prisms

Solids: Prisms (continued)

Have lateral faces that connect the bases

Are named for the angle of their lateral edges

The lateral edges can be “right” or “oblique”

Solids: Prisms (continued)

What shape are the lateral faces?

pentagonal prism hexagonal prisms

Solids: Prisms (continued)

What shape are the lateral faces for these?

Solids: Prisms (continued)

Solids: Prisms (continued)

Right rectangular prism

Oblique rectangular prism

Classify prisms as right or oblique

Classify prisms based on congruent faces

Label a prism’s bases and lateral faces

Prisms TASKS

“SA” stands for surface area

“LA” stands for lateral area (the sum of the areas of lateral faces)

“BA” stands for base area (use appropriate polygon area formula)

Solids: Prisms (continued)

Solids: Prisms (continued)

• LA is made up of the three yellow lateral faces

• BA is one of the red basesFOURTH PROBLEM SET

“V” stands for volume

“BA” stands for base area (use appropriate polygon area formula)

“H” stands for height (be careful if it’s oblique)

Solids: Prisms (continued)

Solids: Prisms (continued)

BA is from one of thecongruent triangles

H is the distance betweenthe congruent triangles

Solids: Prisms (continued)

BA is from one of the congruent pentagon bases

H is the perpendicular distance betweenthe congruent pentagons

Solids: Prisms (continued)

BA is from one of theTriangular bases

H is the long edge of the brown lateral faces

Label a prism’s lateral faces

Find the surface area of a prism

Find the volume of a prism

FIFTH PROBLEM SET

PrismsTASKS (cont'd)

Have 2 identicalfaces (bases)

The two bases are circles

The two bases lie in parallel planes

Solids: Cylinders

Do not have lateral faces; instead there is one, big rectangle wrapped around connecting the bases

Solids: Cylinders (cont'd)

Recall the formula for SA of a prism

Compare it to our cylinder formula

Solids: Cylinders (cont'd)

Recall the formula for V of a prism

Compare it to our cylinder formula

Solids: Cylinders (cont'd)

Label a cylinder’s height and radius

Find the surface area of a prism

Find the volume of a prism

SEVENTH PROBLEM SET

Cylinders TASKS

Discussion question:Which cylinder makes

a better container?

Solids: Cylinders (cont'd)