Right triangle similarity Right triangle similarity Right triangle similarity Right triangle similarity Right triangle similarity Right triangle similarity Right triangle similarity Right triangle similarity Right triangle similarity

3. THE RIGHT TRIANGLE SIMILARITY THEOREM
•IN ANY RIGHT
TRIANGLE, THE
ALTITUDE TO THE
HYPOTENUSE DIVIDES
THE TRIANGLE INTO
TWO RIGHT TRIANGLES,
WHICH ARE SIMILAR TO
EACH OTHER AND TO
THE GIVEN RIGHT
TRIANGLE.
Δ𝐴𝐷𝐵 ~ Δ𝐴𝐵𝐶
Δ𝐵𝐷𝐶 ~ Δ𝐴𝐵𝐶
Δ𝐴𝐷𝐵 ~ Δ𝐵𝐷𝐶

4. WE START WITH ΔABC.

5. WE DRAW ALTITUDE CD TO THE
HYPOTENUSE.

6. THIS DIVIDES THE ORIGINAL
TRIANGLE INTO TWO SMALLER
RIGHT TRIANGLE:

7. THIS DIVIDES THE ORIGINAL
TRIANGLE INTO TWO SMALLER
RIGHT TRIANGLE: ΔDCA

8. THIS DIVIDES THE ORIGINAL
TRIANGLE INTO TWO SMALLER
RIGHT TRIANGLE: ΔBDC

9. THERE ARE A THREE TRIANGLES IN
THE FIGURE BELOW.

10. BIG
Small
Medium

11. BIG
Small
Medium

12. BIG Small
Medium
We orient the three triangles to see
the them clearer.

13. BIG Small
Medium
We can see that the three triangles are
similar to each other.
~
~

14. THE GEOMETRIC MEAN THEOREM
• IN A RIGHT TRIANGLE, THE
ALTITUDE TO THE
HYPOTENUSE IS THE
GEOMETRIC MEAN OF THE
SEGMENTS INTO WHICH IT
DIVIDES THE HYPOTENUSE
AND EACH OF THE LEGS IS
THE GEOMETRIC MEAN OF
THE HYPOTENUSE AND THE
SEGMENT OF THE
HYPOTENUSE ADJACENT TO
THE LEGS.

15. EXAMPLES:

16. 2. FIND THE LENGTH OF THE MISSING
SIDES/SEGMENTS. USE THE GIVEN FIGURE BELOW.