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**Transparency 7**Click the mouse button or press the Space Bar to display the answers.**Example 7-2c**Objective Solve problems involving similar triangles**Example 7-2c**Vocabulary Indirect measurement A technique using proportions to find a measurement**Lesson 7 Contents**Example 1Use Shadow Reckoning Example 2Use Indirect Measurement**Example 7-1a**TREES A tree in front of Marcel’s house has a shadow 12 feet long. At the same time, Marcel has a shadow 3 feet long. If Marcel is 5.5 feet tall, how tall is the tree? A tree in front of Marcel’s house has a shadow 12 feet long Marcel has a shadow 3 feet long Marcel is 5.5 feet Tree 12 feet Marcel 3 feet h feet Tree Write a ratio of the shadows Marcel 5.5 feet Write a ratio of the actual size of Marcel and the tree Define the variable 1/2**Example 7-1a**TREES A tree in front of Marcel’s house has a shadow 12 feet long. At the same time, Marcel has a shadow 3 feet long. If Marcel is 5.5 feet tall, how tall is the tree? Tree 12 feet Write a proportion using the 2 ratios Marcel 3 feet Tree h feet Cross multiply Marcel 5.5 feet h feet 12 feet = 3 feet 5.5 feet 3h 3h = 3h = 12(5.5) 1/2**Example 7-1a**TREES A tree in front of Marcel’s house has a shadow 12 feet long. At the same time, Marcel has a shadow 3 feet long. If Marcel is 5.5 feet tall, how tall is the tree? 12 feet h feet Bring down 3h = = 3 feet 5.5 feet Multiply 12 5.5 3h = 12(5.5) Ask “what is being done to the variable?” 3h = 3h = 66 The variable is being multiplied by 3 Do the inverse operation on both sides of the equal sign 1/2**Example 7-1a**TREES A tree in front of Marcel’s house has a shadow 12 feet long. At the same time, Marcel has a shadow 3 feet long. If Marcel is 5.5 feet tall, how tall is the tree? 12 feet h feet Bring down 3h = 66 = 3 feet 5.5 feet Using the fraction bar, divide both sides by 3 3h = 12(5.5) Combine “like” terms 3h = 3h = 66 Bring down = 3h = 66 Combine “like” terms 3 3 1 h 1 h = 1 h = 22 1/2**Example 7-1a**TREES A tree in front of Marcel’s house has a shadow 12 feet long. At the same time, Marcel has a shadow 3 feet long. If Marcel is 5.5 feet tall, how tall is the tree? 3h = 66 Use the Identify Property to multiply 1 h 3 3 Bring down = 22 1 h = 22 Add dimensional analysis h h = 22 h = 22 feet Answer: The tree is 22 feet tall. 1/2**Example 7-1c**Jayson casts a shadow that is 10 feet. At the same time, a flagpole casts a shadow that is 40 feet. If the flagpole is 20 feet tall, how tall is Jayson? Answer: 5 feet 1/2**Example 7-2a**SURVEYING The two triangles shown in the figure are similar. Find the distance d across the stream. The prompt states the triangles are similar so can write ratios Write a ratio of similar sides C is congruent on both triangles and the right angles are congruent from C 2/2**Example 7-2a**SURVEYING The two triangles shown in the figure are similar. Find the distance d across the stream. Large triangle 60 m CD is similar to CB so write a ratio using their lengths Small triangle 20 m Large triangle 48 m AB is similar to DE so write the 2nd ratio Small triangle d m 48 m 60 m Write a proportion using the 2 ratios = 20 m d m 2/2**Example 7-2a**SURVEYING The two triangles shown in the figure are similar. Find the distance d across the stream. 60 m 48 m = 20 m d m Cross multiply the numbers 60d 60d = 60d = 20(48) Bring down 60d = 60d = 60d = 960 Multiply 20 48 Ask “what is being done by the variable”? The variable is being multiplied by 60 2/2**Example 7-2a**SURVEYING The two triangles shown in the figure are similar. Find the distance d across the stream. 60 m 48 m = 20 m d m Do the inverse on both sides of the equal sign 60d 60d = 20(48) 60d = 60d = 60d = 960 Bring down 60d = 960 60d = 960 Using the fraction bar, divide both sides by 60 60 60 2/2**Example 7-2a**SURVEYING The two triangles shown in the figure are similar. Find the distance d across the stream. 60d = 960 60 60 Combine “like” terms 1 d 1 d = 1 d = 16 Bring down = d d = 16 Combine “like” terms Use the Identify property to multiply 1 d Bring down = 16 2/2**Example 7-2a**SURVEYING The two triangles shown in the figure are similar. Find the distance d across the stream. 60d = 960 60 60 Add dimensional analysis 1 d 1 d = 1 d = 16 d d = 16 d = 16 m Answer: The distance across the stream is 16 meters. 2/2**Example 7-2c*** SURVEYING The two triangles shown in the figure are similar. Find the distance d across the river. Answer: 7 feet 2/2**End of Lesson 7**Assignment