Indirect Measurement

Warm-Up Solve each proportion X X X 4. X = = == X = 45 X = 20 X = 2 X = 4

What we are doing… Learn to find measures indirectly by applying the properties of similar figures.

Indirect Measurement…. F EG A BC Notice how all angles are congruent. A BC A BC A BC A B A BC Notice what happens as we turn the triangle. Which angle corresponds with angle E? Which angle corresponds with angle F? B A

Example 1; Triangles ABC and EFG are similar. Find the length of side EG. B AC 3 ft 4 ft F EG 9 ft X Triangles ABC and EFG are similar.

1. Vilma wants to know how wide the river near her house is. She drew a diagram and labeled it with her measurements. How wide is the river? Question 1:

The diagram: W 7 m 21 m 15 m Work…

Question 2: Julie wants to know how far it is from her house to the big oak tree. She drew a diagram and labeled it with her known measurements. How far is the tree from her house?

Diagram…. 5 ft 6 ft4 ft 24 ft 16 ft Work…..

Question 3 A yardstick casts a 2-ft shadow. At the same time, a tree casts a shadow that is 6 ft long. How tall is the tree? ?? 6 ft 3 ft 2 ft

Question 4; A 30 ft building casts a shadow that is 18 ft long. A nearby tree casts a shadow that is 3 ft long. How tall is the tree? 30 ft 18 ft 3 ft ?????

Question 5 Triangles with triangles… AC = 30 DC = 20 BE = 4 AB = ? E B D CA

Question 6; E B D CA AC = 24 DC = ? BE = 8 AB = 4