Over Lesson 6–8 A.A B.B C.C D.D 5-Minute Check 1 The figures are similar. Find the missing measure. Lesson 6-7 The figures are similar. Find the missing.

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Presentation transcript:

Over Lesson 6–8 A.A B.B C.C D.D 5-Minute Check 1 The figures are similar. Find the missing measure. Lesson 6-7 The figures are similar. Find the missing measure.

Splash Screen

Then/Now You have already used similar figures to determine missing measures. (Lesson 6–7) Solve problems involving indirect measurement using shadow reckoning. Solve problems using surveying methods.

Vocabulary indirect measurement Using the properties of similar triangles to find measurements that are difficult to measure directly

Example 1 Use Shadow Reckoning MONUMENTS Suppose the San Jacinto Monument in LaPorte, Texas, casts a shadow of 285 feet. At the same time a nearby tourist, who is 5 feet tall, casts a 2.5-foot shadow. How tall is the San Jacinto Monument? UnderstandYou know the lengths of the shadows and the height of the tourist. You need to find the height of the San Jacinto Monument. Plan Write and solve a proportion.

Example 1 Use Shadow Reckoning (Drawings below not to scale). 285 feet 5 feet 2.5 feet How tall is this?

Example 1 Use Shadow Reckoning Solve tourist’s shadow monument’s shadow tourist’s height monument’s height 2.5 ● h = 285 ● 5Find the cross products. 2.5h=1425Multiply. h=570Divide each side by 2.5. Answer: The height of the San Jacinto Monument is 570 feet.

Example 1 Use Shadow Reckoning CheckThe tourist’s height is 2 times the length of his or her shadow. The monument should be 2 times its shadow, or 2 ● 285, which is 570 feet.

A.A B.B C.C D.D Example 1 A.1200 feet B.480 feet C.83.3 feet D.13.3 feet BUILDING A man standing near a building casts a 2.5-foot shadow at the same time the building casts a 200-foot shadow. If the man is 6 feet tall, how tall is the building?

Example 2 Find Missing Measures MAPS In the figure, ΔPQT ~ ΔPRS. Find the distance across the lake. Since the figures are similar, corresponding sides are proportional.

Example 2 Find Missing Measures Answer: The distance across the lake is 28.8 meters. Write a proportion. PR = 60, PQ = 25, RS = x, and QT = 12. Find the cross products. Multiply. Divide each side by 25.

A.A B.B C.C D.D Example 2 MAPS In the figure, ΔMNO is similar to ΔQPO. Find the distance across the park. A.1.9 mi B.3.1 mi C.4.8 mi D.5.0 mi

End of the Lesson