2-8 Vocabulary Similar figures Scale drawing Scale Scale model

2-8A Similar Figures Algebra 1

Similar Symbol   Similar figures have the same shape but not necessarily the same size. In similar figures, the measures of corresponding angles are EQUAL, and the ratios of corresponding side lengths are EQUAL.

Example 1 In the diagram, LM = 4, LN = 3, NQ = 10, PN =8 a.) What are the corresponding parts? b.) Find P c.) Find MN and QM L M N Q Use Extra example #1 picture

Example 2 Applying Similarity A 6 ft tall man is standing next to a flagpole. The man’s shadow is 17.5 ft. What is the flagpole’s height?

2-8 B Scale drawing A drawing that is similar to an actual object or place. In a scale drawing, the ratio of any length on the drawing to the actual length is always the same. This ratio is called the scale of the drawing.

Example 1 One inch represents 12 miles on a map. If the distance between the two buildings is 4 inches on the map, what is the actual distance?

Example 2 If you know that the actual distance between two cities is 250 miles and the cities are 2 inches apart on a map, how can you find the scale of the map?

Example 3 A model of a new campus building is 5 inches tall. If 1 inch represents 8.5 ft, how tall will the building be?

Ex. 4 A scale model of a building is 6 inch tall. The scale of the model is 1 in.: 50 ft. How tall is the actual building?

Assignment

Postulate 25 Angle – Angle (AA) Similarity Postulate If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar.

Determining Similarity Ex. 2) Determine whether the triangles can be proved similar. If they are similar, then write a similarity statement. If they are not similar, explain why. Use Extra Example 2 picture.

Slope Slope formula #29?

Using Algebra Ex. 3 – Use points G & J in the diagram below to find the slope of the line containing GJ. Name five other segments whose endpoints could be used to find the slope of the line.

Find the value of the variable Ex. 4) Find y. Use picture for #6 & 7

Generalization of Theorem 8.1 If two polygons are similar, then the ratio of any two corresponding lengths (such as altitudes, medians, angle bisector segments, and diagonals) is equal to the scale factor of the similar polygons.

Similar Triangles Ex. 5) The segments in blue are special segments in the similar triangles. Find the value of the variable. Use #45 as example