Real-world examples of similar figures for Grade 8 students

📚 Quick Study Guide

📐 Similar Figures: Figures that have the same shape but different sizes. 比例 Corresponding Sides: Sides that are in the same relative position in similar figures. 📏 Scale Factor: The ratio of the lengths of corresponding sides in similar figures. If figure A is similar to figure B, then: $Scale\ Factor = \frac{Length\ of\ a\ side\ in\ figure\ B}{Length\ of\ the\ corresponding\ side\ in\ figure\ A}$ 💡 Key Property: Corresponding angles in similar figures are equal. ✍️ Example: If two triangles are similar, and one has sides 3, 4, and 5, a similar triangle could have sides 6, 8, and 10 (scale factor of 2).

🧪 Practice Quiz

1. A photo is 4 inches wide and 6 inches tall. If it's enlarged to be 12 inches tall, how wide will the enlarged photo be to maintain similarity?
   1. 6 inches
   2. 8 inches
   3. 10 inches
   4. 14 inches
2. A map has a scale of 1 inch = 25 miles. Two cities are 3.5 inches apart on the map. What is the actual distance between the cities?
   1. 75 miles
   2. 87.5 miles
   3. 90 miles
   4. 100 miles
3. Triangle ABC is similar to triangle XYZ. If angle A is 60 degrees and angle B is 80 degrees, what is the measure of angle X?
   1. 40 degrees
   2. 60 degrees
   3. 80 degrees
   4. 100 degrees
4. A building casts a shadow that is 30 feet long. A nearby 5-foot tall pole casts a shadow that is 3 feet long. How tall is the building?
   1. 40 feet
   2. 45 feet
   3. 50 feet
   4. 55 feet
5. Two rectangles are similar. The first rectangle is 5 cm wide and 10 cm long. The second rectangle is 15 cm wide. How long is the second rectangle?
   1. 20 cm
   2. 25 cm
   3. 30 cm
   4. 35 cm
6. A triangular garden has sides of 8 feet, 12 feet, and 16 feet. A similar garden is to be built with the shortest side being 6 feet. What is the length of the longest side of the new garden?
   1. 8 feet
   2. 10 feet
   3. 12 feet
   4. 14 feet
7. A blueprint of a house is drawn to a scale of 1 inch = 4 feet. If a room is 12 feet long, how long will it be on the blueprint?
   1. 2 inches
   2. 3 inches
   3. 4 inches
   4. 5 inches