1. Bell Quiz

2. Objectives Learn to write and solve problems using proportions.

3. Proportions Proportions are frequently used to solve problems in mathematics. Proportional reasoning can be applied in many situations, including reading and drawing maps, architecture, and construction. Solving problems in these situations require knowledge of similar figures.

4. Similar Figures If two geometric objects or figures are similar, they have the same shape but are not necessarily the same size. The triangles below are similar:

5. Similar Figures When two figures are similar, they have sides and angles that correspond. Corresponding sides and angles are found using the order of the letters in the similarity statement. In the triangles from the previous slide, angles A and D correspond, angles B and E correspond, and angels C and F correspond. Corresponding angles of similar figures are congruent, or have the same measure.

6. Proportions Sides of similar figures also correspond. In the previous example, AC and DE correspond, BC and EF correspond, and AC and DF correspond. Corresponding sides of similar figures do not have to be congruent. However they do have to be in proportion. The ratio of all the pairs of corresponding sides must be the same.

7. Example 1 Finding Measures in Similar Figures

8. Lesson Practice

10. Example 2 Using Indirect Measurement A radio tower casts a shadow 10 feet long. A woman who is 5.5 feet tall casts a shadow 4 feet long. The triangle drawn with the tower and its shadow is similar to the triangle drawn with the woman and her shadow. How tall is the radio tower?

11. Lesson Practice The side of a building casts a shadow 21 meters long. A statue that is 5 meters tall casts a shadow 4 meters long. The triangles are similar. How tall is the building?

12. Scale Drawing A scale drawing is a drawing that reduces or enlarges the dimensions of an object by a constant factor. Maps and blueprints are examples of scale drawings. The scale is a ratio showing the relationship between a scale drawing or model and the actual object

13. Example 3 Locating x- and y- intercepts on a Graph A desk is designed to have three drawers on the right side. In the scaled design drawing, the width of the drawers is 4 centimeters. If the scale of the drawing is 1 cm: 7cm, how wide will the actual desk drawers be?

14. Lesson Practice The scale drawing of the kitchen tabletop has dimensions 5 inches by 2.5 inches. If the scale factor of the drawing to the actual table is 1 in. : 18 in., what are the dimensions of the actual table?

15. Ratios

16. Example 4 Application: Changing Dimensions A dartboard is composed of concentric circles. The radius of the smallest inner circle is 1 inch, and with each consecutive circle, the radius increase by 1 inch. a.What is the ratio of the circumference of the two inner circles to the circumference of the outermost circle? b.What is the ratio of the area of the two inner circles to the area of the outermost circle.

17. Lesson Practice Small toy cars are constructed using a scale factor of 1 in : 64 in. What is the ratio of the areas of the toy car and the actual car.