Upcoming SlideShare
×

# Right Triangle Similarity

21,801 views
21,076 views

Published on

Published in: Education
8 Likes
Statistics
Notes
• Full Name
Comment goes here.

Are you sure you want to Yes No
Your message goes here
• tnx slideshare..this site is indeed beneficial!.more power!.

Are you sure you want to  Yes  No
Your message goes here
• i do appreciate the presentation. It really is very helpful...thanks

Are you sure you want to  Yes  No
Your message goes here
• the site really very helpful to me, especially to my class. thanks alot.

Are you sure you want to  Yes  No
Your message goes here
Views
Total views
21,801
On SlideShare
0
From Embeds
0
Number of Embeds
757
Actions
Shares
0
388
3
Likes
8
Embeds 0
No embeds

No notes for slide

### Right Triangle Similarity

1. 1. SIMILARITY IN RIGHT TRIANGLES<br />
2. 2. We start with ΞABC.<br />
3. 3. We draw altitude CD to the hypotenuse.<br />
4. 4. This divides the original triangle into two smaller right triangle:<br />
5. 5. This divides the original triangle into two smaller right triangle: ΞDCA<br />
6. 6. This divides the original triangle into two smaller right triangle: ΞBDC<br />
7. 7. There are a three triangles in the figure below.<br />
8. 8. Big<br />Medium<br />Small<br />
9. 9. Big<br />Medium<br />Small<br />
10. 10. We orient the three triangles to see the them clearer.<br />Big<br />Small<br />Medium<br />
11. 11. We can see that the three triangles are similar to each other. <br />~<br />~<br />Big<br />Small<br />Medium<br />
12. 12. SIMILARITY IN RIGHT TRIANGLES<br />
13. 13. Parts of a right triangle incorporated with the altitude<br />C<br />Leg adjacent to DB<br />Leg adjacent to AD<br />A<br />B<br />D<br />Segments of the hypotenuse AD and DB<br />
14. 14. Right Triangle Similarity Theorem<br />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.<br />C<br />A<br />B<br />D<br />οABC ~ οACD ~ οCBD<br />
15. 15. Geometric Mean-Altitude Theorem 1<br />The length of the altitude to the hypotenuse is the geometric mean of the lengths of the segments of the hypotenuse.<br />C<br />A<br />B<br />D<br />ππππ=ππππ<br />Β <br />ππ=ππΓππ<br />Β <br />
16. 16. Geometric Mean-Altitude Theorem 2<br />The altitude to the hypotenuse to a right triangle intersects it to that the length of each leg us the geometric mean of the length of its adjacent segment of the hypotenuse and the length of the entire hypotenuse<br />BACB=CBBD<br />Β <br />ABCA=CAAD<br />Β <br />ππ=ππΓππ<br />Β <br />ππ=ππΓππ<br />Β <br />
17. 17. Summary of theGeometric Mean β Altitude Theorem<br />b<br />a<br />h<br />m<br />n<br />c<br />π=π¦+π§<br />Β <br />π=π¦Γπ<br />Β <br />π‘=π¦Γπ§<br />Β <br />π=π§Γπ<br />Β <br />
18. 18. Solve for the other missing lengths given only two measurements.<br />a = 4, b = 6<br />a = 8, c = 10<br />a = 5, m = 7<br />a = 9, n = 6<br />a = 12, h = 9<br />b = 6, c = 15<br />b = 8, m = 9<br />b = 4, n = 3<br />b = 11, h = 8<br />c = 18, m = 12<br />c = 15, n = 8<br />c = 20, h = 6<br />m = 12, n = 8<br />m = 9, h = 12<br />n = 10, h = 12<br />
19. 19. Solve for the other missing lengths given only two measurements.<br />a = 4, b = 6<br />a = 8, c = 10<br />a = 5, c = 8<br />a = 9, m = 6<br />a = 12, h = 9<br />b = 6, c = 15<br />b = 12, n = 9<br />b = 4, n = 3<br />b = 10, h = 6<br />b = 11, h = 8<br />c = 18, m = 12<br />c = 15, n = 8<br />c = 20, m = 6<br />m = 12, n = 8<br />m = 9, h = 12<br />n = 10, h = 12<br />a = 9, m = 6<br />c = 18, m = 12<br />
20. 20. Relating to the Real WorldRecreation<br />At the parking lot of a State Park, the 300-m path to the snack bar and the 400-m path to the boat rental shop meet at a right angle. Marla walks straight from the parking lot to the ocean. How far is Marla from the snack bar?<br />WHICH IS STRONGER? TRIANGLE OR QUADRILATERAL?<br />