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# 8 1 Similarity In Rt Tri

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### 8 1 Similarity In Rt Tri

1. 1. Right Triangles 8-1 Similarity in Right Triangles
2. 2. Review Means Extremes Means
3. 3. Geometric Mean The geometric mean between a and b is x if you do this: What is x?
4. 4. What is the geometric mean between 2 and 18? <ul><li>9 </li></ul><ul><li>6 </li></ul><ul><li>20 </li></ul><ul><li>8 </li></ul>0 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
5. 5. Theorem <ul><li>If the altitude is drawn to the hyp. of a right triangle, then the two triangles formed are similar to the original triangle and to each other. </li></ul>
6. 6. Corollary <ul><li>The length of the altitude is the geometric mean between the segments of the hypotenuse </li></ul>
7. 7. Corollary 2 <ul><li>Each leg is the geometric mean between the hyp. And the segment of the hyp. that is adjacent to that leg </li></ul>
8. 8. u is the geometric mean between __ and __. <ul><li>s,r </li></ul><ul><li>k,r </li></ul><ul><li>k,s </li></ul><ul><li>v,u </li></ul><ul><li>t,r </li></ul>u k t v s r 0 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
9. 9. t is the geometric mean between __ and __. <ul><li>s,r </li></ul><ul><li>k,r </li></ul><ul><li>k,s </li></ul><ul><li>t,u </li></ul>u k t v s r 0 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
10. 10. v is the geometric mean between __ and __. <ul><li>s,r </li></ul><ul><li>k,r </li></ul><ul><li>k,s </li></ul><ul><li>t,v </li></ul>u k t v s r 0 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
11. 11. v is the geometric mean between __ and __. <ul><li>s,r </li></ul><ul><li>k,r </li></ul><ul><li>k,s </li></ul><ul><li>t,v </li></ul>u k t v s r 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 7
12. 12. SPICSA <ul><li>Page 288 2-24 even </li></ul>