5-8. Scale Drawings and Models

Scale drawing or a scale model – used to represent an object that is too large or too small to be drawn or built at actual size.

Scale – ratio of a given length on the drawing or model to its corresponding length on the actual object.

*Scales are written unit length on the drawing or model first.

Examples:1 inch = 3 feet 1 cm = 2 mm

Example Pages.1b. The length of a model bridge is 16 inches. The actual length of the bridge is 50 yards. What is the scale of the model?

Scale factor – scale with the same units written without units

Example: 1 inch = 10 feet

Example Page 225.2. A map of a natural history museum shows that a dinosaur exhibit room is 7.25 inches wide. If the scale on the map is 1 inch = 8 feet, a) what is the width of the actual exhibit room? b) what is the scale factor of the map?

Example Page 226.3. An architect is designing a school courtyard that is 45 feet long and 30 feet wide. Make a scale drawing of the courtyard.

Use a scale of 0.5 inch = 10 feet. Use 𝟏

𝟒-inch grid paper.

5-9. Similar Figures

Similar figures – are figures that have the same shape but not necessarily the same size.

If two figures are similar:● the corresponding angles are congruent,

or have the same measure● the corresponding sides are proportional

and opposite corresponding angles

XB

A C Y Z

1b. Page 233

2. page 234. A rectangular blue tile has a length of 4.25 inches and a width of 6.75 inches. A similar red tile has a length of 12.75 inches. What is the width of the red tile?

2. Page 234 Find x.

Seatwork: To be collected after 30 minutes.

Copy and answer. Show complete work.

Pages 235 – 236

Numbers 4 to 14, even only.

5-10. Indirect Measurement

Indirect measurement allows for us to use properties of similar triangles to find measurements that are difficult to measure directly.

Examples: - using shadow reckoning- using similar triangles to measure across a river

1. page 238. Suppose a bell tower casts a 27.6-foot shadow at the same time a nearby tourist casts a 1.2-foot shadow. If the tourist is 6 feet tall, how tall is the tower? Draw a diagram.

2. page 239. In the figure ∆QRS ~ ∆URT. Find the distance from the cabin to the Mess Hall. Cabin

Q

x yd=?Mess Hall

46 yd T S 138 yd R

60yd

U

9. page 240. A biplane starts to take off from the beginning of a runway. When the plane is level with the end of the runway, it is 500 feet above the ground. A bird is flying in the same direction. It is 8 feet above the ground and 15 feet from the beginning of the runway.

a. Draw a diagram of the situation.b. Write and solve a proportion to find how far the plane is

from the beginning of the runway.

9. page 240. A biplane starts to take off from the beginning of a runway. When the plane is level with the end of the runway, it is 500 feet above the ground. A bird is flying in the same direction. It is 8 feet above the ground and 15 feet from the beginning of the runway.

a. Draw a diagram of the situation.b. Write and solve a proportion to find how far the plane is from the

beginning of the runway.

biplane

500 ft bird

8 ft

15 ft

end of the runway x beginning of the runway