CHAPTER 8: RIGHT TRIANGLES 8.1 SIMILARITY IN RIGHT TRIANGLES

RIGHT TRIANGLE Recall that triangles can be named by angle measures and side lengths. A right triangle is identified by angle measure and has the following characteristics: 1 right angle (90° angle) 2 acute angles (angles less than 90°) A hypotenuse and 2 legs

RIGHT TRIANGLE A right triangle is shown below with all sides and angles named: Acute angle hypotenuse leg Right angle Acute angle leg

RADICALS The solutions to problems involving radicals should always be written in simplest radical form: No perfect square factor other than 1 is under the radical sign. No fraction is under the radical sign. No fraction has a radical in its denominator.

EXAMPLES    

PROPORTIONS  

GEOMETRIC MEAN  

EXAMPLE  

YOU TRY Find the geometric mean: Between 5 and 10 Between 6 and 8  

SIMILARITY IN POLYGONS Remember that if two polygons are similar, then the following holds true: Corresponding angles are congruent; Corresponding sides are in proportion. We use the symbol ~ to represent similarity.

THEOREM 8-1 THEOREM 8-1 If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed are similar to the original triangle and to each other. ∆ACB ~ ∆ARC ~ ∆CRB C A B R

COROLLARY 1   C A B R

COROLLARY 2   C B A R

H EXAMPLE 2 E R J 4 EJ = RE = RH = HE =  

H PRACTICE E 9 J 16 R 12 25 20 15 HJ = RE = RH = HE =

CLASSWORK/HOMEWORK 8.1 Assignment Pgs. 287-288, Classroom Exercises 2-16 even Pgs. 288-289, Written Exercises 2-38 even