1. GEOMETRY 5.5
GEOMETRY 5.5
Review of 5.4 – Angles & Sides of a Triangle

2. GEOMETRY 5.5
Review of 5.4 – Angles & Sides of a Triangle

3. GEOMETRY 5.5
Review of 5.4 – Angles & Sides of a Triangle

4. GEOMETRY 5.5
Review of 5.4 – Angles & Sides of a Triangle

5. The PERPENDICULAR segment from a Point to a LineIS
the SHORTEST Segment from the Point to the Line.
Given: P
Prove: 2 1 j Q A

6. GEOMETRY 5.5

7. GEOMETRY 5.5

8. GEOMETRY 5.5

9. GEOMETRY 5.5
GEOMETRY 5.5

10. GEOMETRY 5.5
GEOMETRY 5.5
To Determine whether 3 lengths could make a Triangle:

11. GEOMETRY 5.5
GEOMETRY 5.5
To Determine whether 3 lengths could make a Triangle:
ADD the Two Smallest Lengths (a + b)

12. GEOMETRY 5.5
GEOMETRY 5.5
To Determine whether 3 lengths could make a Triangle:
ADD the Two Smallest Lengths (a + b)
Compare the SUM to the Longest Length (c)

13. GEOMETRY 5.5
GEOMETRY 5.5
To Determine whether 3 lengths could make a Triangle:
ADD the Two Smallest Lengths (a + b)
Compare the SUM to the Longest Length (c)
To make a Triangle: a + b > c

14. GEOMETRY 5.5

15. GEOMETRY 5.5

16. GEOMETRY 5.5

17. GEOMETRY 5.5

18. x + a > b a + b > x To determine the RANGE of possible Lengths
of the 3rd side of a Triangle:
Given length a and b, with a < b
Find the RANGE of the third side, x
Lower Limit: Upper Limit:
x + a > b a + b > x

19. GEOMETRY 5.5

20. GEOMETRY 5.5
REMEMBER:
Distance between 2 points on the graphing plane:

21. GEOMETRY 5.5

22. GEOMETRY 5.5

23. GEOMETRY 5.5

24. GEOMETRY 5.5
AB + BC > AC
BC + AC > AB
AC + AB > BC

25. GEOMETRY 5.5
GEOMETRY 5.5
PQ + QR > PR
QR + PR > PQ
PR + PQ > QR

26. GEOMETRY 5.5 R O
Given: Triangle ROS
Prove: SO + OR > RS S

27. GEOMETRY 5.5
GEOMETRY 5.5 R O
Given: Triangle ROS T
Prove: SO + OR > RS S
Start: Draw segment OT
so that OT = SO

28. GEOMETRY 5.5 D
Given:
Prove: BD + DC > AC 1 2 A B C

29. GEOMETRY 5.5
Given: D
Prove: BE + ED + AC > DC E 1 2 A B C

30. GEOMETRY 5.5

31. GEOMETRY 5.5