Using Similar Triangles in Real-World Problems

This lesson focuses on applying the concept of similarity in real-world problems. Students learn to use similar triangles to measure objects that are difficult to measure directly, such as flagpoles, buildings, and lakes. The lesson includes exercises on using mirrors to measure building heights, determining the width of a lake using parallel lines, and predicting tree growth for shade. The teacher emphasizes the importance of understanding the relationships between similar triangles and using ratios to find missing measurements.

What is the main focus of the lesson on modeling with similarity?

• Applying similarity concepts to real-world problems

• Learning about different types of triangles

• Using similar triangles to solve algebraic equations

• Understanding the history of geometry

In the flagpole problem, what is the length of the shadow of the flagpole?

• 25 feet

• 10 feet

• 15 feet

• 20 feet

How do you determine the height of a building using a mirror and similar triangles?

• By calculating the area of the triangles

• By using the AA criterion for similarity

• By measuring the distance from the mirror to the building

• By measuring the angle of elevation

What is the distance from the mirror to the building in the building height measurement exercise?

• 5.3 feet

• 1742.8 feet

• 1750 feet

• 7.2 feet

In the lake width measurement exercise, what is the length of segment DE?

• 5 feet

• 22 feet

• 7 feet

• 15 feet

How do you find the widest part of the lake using similar triangles?

• By measuring the height of the surrounding trees

• By calculating the perimeter of the lake

• By using the AA criterion and corresponding angles

• By measuring the depth of the lake

What is the required height of the tree to provide shade to the house?

• 16 feet

• 26.5 feet

• 32 feet

• 53 feet

How many years will it take for the tree to grow to the required height if it grows 2.5 feet per year?

• 12 years

• 10 years

• 7.8 years

• 5 years

What is the significance of using similar triangles in real-world problems?

• They are used to measure angles accurately

• They help in calculating the area of complex shapes

• They provide a method to calculate volumes

• They simplify the process of finding unknown lengths

Which of the following is NOT a step in solving the tree height problem?

• Determining the growth rate of the tree

• Using the AA criterion for similarity

• Measuring the circumference of the tree

• Calculating the shadow length