SUBJECT Geometry UNIT TITLE Similarity Topic: 8-4 Similarity in Right Triangles Objective: To find and use relationships in similar right triangles Core Content for Assessment: MA-11-3.1.6 Students will apply the concepts of congruence and similarity to solve real world problems Materials/Resources: Right Triangle Activity worksheet, calculators, index cards, scissors Warm Up/Bell Ringer/Do Now: Solve each proportion: x 18 2 x 15 18 1. 2. 3. 8 24 3 7 4 x 4. 51 17 x 13 Procedures: 1. Warm Up 2. Check HW as appropriate 3. Investigation: Similarity in Right Triangles 4. Discuss theorem discovered from investigation Thm: The altitude to the hypotenuse of a right triangle divides the triangle into two triangles that are similar to the original triangle and to each other. 5. Geometric Mean of a and b – the positive number x such that a x -> x2 = ab -> x ab x b 6. Examples: Find the Geometric Mean a. 4 and 25 4 and 18 4 x 4 x x 25 x 18 X2=100 x2=72 X=10 x= 72 = 6 2 7. Corollary: The length of the altitude to the hypotenuse of a right triangle is the geometric mean of the lengths of the segment of the hypotenuse. a x x b X a b ex. Find x: a. a=3 b=27 b. a=5 b=25 8. Corollary: The altitude to the hypotenuse of a right triangle separates the hypotenuse so that the length of each leg of the triangle is the geometric mean of the length of the adjacent hypotenuse segment and the length of the hypotenuse. x x a b a x2=a(a+b) b x2=b(a+b) ex. Solve for the variable x 8 10 3 9 6 a b x 21 7 13 29 20 9. Class work as appropriate a b Lesson Assessments: Assign HW as appropriate Class work check Investigating Similar Right Triangles 1. Cut an index card along one of its diagonals. 2. On one of the right triangles mark the right angle. 3. With the other right triangle fold in the altitude. Cut this triangle down the altitude. You should now have three right triangles. 4. Compare the 3 right triangles. What special property do they share?