Find that Angle
Explain the relationship two vertical angles have to each other
two VERTICAL angles are EQUAL to each other
What 3 tools do you need to draw triangles?
How many triangles can be drawn from this compass distance? How do you know?
compass, protractor, ruler
2 triangles can be drawn as the compass circle intersects the blue dotted line in 2 different places.
Tell the surface area of the following rectangular prism. Show your work.
684 square inches
Tell what the units are for volume different for surface area. Explain why they are different.
units for surface area = units squared
units for volume = units cubed
units are different because for surface area 2 units are multiplied together and for volume, 3 units are multiplied together.
What is the shape of the slice from the trianglular prism?
rectangle
Name 3 different ways that angles can relate to each other
Vertical = two opposite angles are equal
Complementary = add together to be 90
Supplementary = add together to be 180
what angles amount are three interior angles of triangles ALWAYS equal to?
three interior triangle angles = 180
A metal box that is in the shape of rectangular prism has the following dimensions. The length is 9 inches, width is 2 inches, and height is 1 1/2 inches. Find the surface area of the box.
69 square inches
Volume of triangular prism with rectangular hole. units are in inches.
Volume of trianglular prism
½ x 16 x 13 x 14 = 1456
Volume of circular prism
6 x 3 x 14 = 252
Subtract the two volumes
1456 - 252 = 1204 inches cubed
What is the shape and number of sides for the slice of the rectangular prism?
4 sided rectangle
Find the unknown Angle KJL
angle KJL = 29
180-57 = 123
180 - 123 - 28 = angle KJL = 29
What are 5 rules for identical (congruent) triangles?
ASA
SAS
SSS
AAS
SSA (generally not yet can be IF angle is larger than 90)
Draw a picture of an equilateral (all equal sides) triangular prism.
Then tell the formula for finding the surface area of this equilateral trianglar prism?
3 identical rectangular sides = 3( length x width )
2 identical triangle sides = 2 ( 1/2 x length x width)
all added together to make total surface area
Cherise is setting up her tent. Her tent is in the shape of a trapezoidal prism shown below. What is the volume of the tent.
middle rectangular prism
4x4x9 = 144 ft cubed
triangluar prism (left and right)
½ x 1 x 4 x9 = 18 ft cubed
½ x 1 x 4 x 9 = 18 ft cubed
Total volume = 144+18+18 = 180ft cubed
What is the number of sides and shape of the slice from the rectangular prism?
6 sided hexagon
Find unknown angle WXZ
Write your equation including the steps to find the answer.
angle WXZ = 123
180 - 58 - 65 = angle YXZ
angle YXZ = 57
180 - 57 = angle WXZ = 123
Tell if these triangles are congruent (unique)?
If yes, tell what rule proves they are congruent.
If no, tell what rule they don't have.
YES
SAS rule
Find the surface area of the house
triangular pyramid surface area = 1/2 x 5 x 5 = 12/5 ft squared
4 triangle sides = 4 x 12/5 = 50 ft squared
rectangle prism surface area =
front = 4 x 12 = 48 ft squared
back = 4 x 12 = 48 ft squared
side = 4 x 5 = 20 ft squared
side = 4 x 5 = 20 ft squared
bottom = 12 x 5 = 60 ft squared
top = 7 x 5 = 35 ft squared
add all areas together = 50 + 48 + 48+ 20 + 20 + 60 + 35 = 281 ft squared
Find volume for the three rectangular prisms. Make sure units are correct.
Volume = 74 cubic ft.
What is the total area of the shape?
18x squared
find amounts of 3 angles using drawing.
Write your equation and show your work.
x+ 3 + x - 1 + x + 1 = 90
3x + 3 = 90
3x = 87
x = 29
angle 1 = 29 + 3 = 32
angle 2 = 29 - 1 = 28
angle 3 = 29 + 1 = 30
Tell if these two triangles are congruent (or not).
If yes, tell what rule proves they are congruent.
If no, tell what rule they are not following.
NO
SSA is not generally a rule for congruence. Angle is not larger than 90.
Find surface area of the green and blue bird house before the hole was drilled.
Blue triangle
½ 30 x 8 (x2) = 240cm2
2 blue rectangles = 24cm x 17cm (x2) = 816cm2
Front and back = 30 x 18 (x 2) = 1080cm2
Two sides = 24 x 18 (x2) = 864 cm2
Bottom = 30 x 24 = 720cm2
Add all together = 3720cm2
What is the volume of a Prism with Circular hole ?
Prism volume =25 x 25 x 30 = 18750
Circular prism volume = 3.14 x 4 x 4 x 30 = 1507.2
Subtract the two volumes =
18750 - 1507.2 = 17242.8 cm cubed
What is the percent of the single large square area to the total area?
9xsquared / 16xsquared = 0.5625
0.5625 x100 = 56.25%