1. CHAPTER 8: RIGHT TRIANGLES
8.1
SIMILARITY IN RIGHT TRIANGLES

2. 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

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

4. 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.

5. EXAMPLES

6. PROPORTIONS

7. GEOMETRIC MEAN

8. EXAMPLE

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

10. 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.

11. 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

12. COROLLARY 1 C A B R

13. COROLLARY 2 C B A R

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

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

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