1. Warm-up
Take a copy of the white paper and get busy!!!

2. Warm-up

3. Warm-up
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4. Agenda Homework Review Section 5-4 Section 5-5
Flatland – 0 to 3 dimensions – Euclidean Geometry
Edwin A Abbott – Headmaster
1884
Flatterland – Euclidean & Non-Euclidean, Physics
Ian Stewart
2001

5. 5-3 Study Guide Flatland – 0 to 3 dimensions – Euclidean Geometry
Edwin A Abbott – Headmaster
1884
Flatterland – Euclidean & Non-Euclidean, Physics
Ian Stewart
2001

6. 5-3 Practice Flatland – 0 to 3 dimensions – Euclidean Geometry
Edwin A Abbott – Headmaster
1884
Flatterland – Euclidean & Non-Euclidean, Physics
Ian Stewart
2001

7. 5-3 Practice Flatland – 0 to 3 dimensions – Euclidean Geometry
Edwin A Abbott – Headmaster
1884
Flatterland – Euclidean & Non-Euclidean, Physics
Ian Stewart
2001

8. 5-3 Practice Flatland – 0 to 3 dimensions – Euclidean Geometry
Edwin A Abbott – Headmaster
1884
Flatterland – Euclidean & Non-Euclidean, Physics
Ian Stewart
2001

9. 5-3 Practice Flatland – 0 to 3 dimensions – Euclidean Geometry
Edwin A Abbott – Headmaster
1884
Flatterland – Euclidean & Non-Euclidean, Physics
Ian Stewart
2001

10. Given: Points A, B and C are on line l Point P is not on l PB < PC
Prove: mPCB  90 A B C l 1. 2. 3. 4. P

11. Given: Points A, B and C are on line l Point P is not on l PB < PC
Prove: mPCB  90 A B C l
Assume PCB = 90
Then PC  l
 PC < PB (Contradiction)
 PCB  90 P

12. 4

13. 5-4 Side & Angle Inequalities
Theorem 5-9
If one side of a triangle is longer than another side, then the angle opposite the longer side has a greater measure than the angle opposite the shorter side.

14. 5-4 Side & Angle Inequalities
Theorem 5-10
If one angle of a triangle has a greater measure than another angle, then the side opposite the greater angle is longer than the side opposite the lesser angle.

15. 5-4 Side & Angle Inequalities
Theorem 5-11
The perpendicular segment from a point to a line is the shortest segment from the point to the line.

16. 5-5 Triangle Inequalities
Build a triangle
Get rulers and plain paper
Draw ABC
where AC = 10 in
and AB = 6 in
and BC = 4 in

17. Section 5-4 14 16 7 7 22 22

18. Section 5-4

19. 5-5 Triangle Inequalities
If two sides of a triangle are 5 and 12 what are the possible values for the size of the third side?

20. Theorem 5-13 SAS Inequality Hinge Theorem
If two sides of one triangle are congruent to two sides of another triangle and the included angle in one triangle has a greater measure than the included angle in the other, then the third side of the first triangle is longer than the third side in the second triangle.

21. Theorem 5-14 SSS Inequality
If two sides of one triangle are congruent to two sides of another triangle and the third side in the first triangle has a greater measure than the third side in the other, then the angle between the pair of congruent sides in the first triangle is larger than the included angle in the second triangle.

22. Example

23. Examples

24. Examples

25. Given:
mP > mR
Prove: m2 > m1 1. 1. 2. 2. 3. 3. 4. 4. 5. 5.

26. Given: mP > mR Prove: m2 > m1 1. 1. Given
2. Reflexive property 2. 3.
3. Given 4.
4. Larger  implies larger side 5.
5. SSS Inequality

27. Answers Ahead

28. 5-4 Study Guide Flatland – 0 to 3 dimensions – Euclidean Geometry
Edwin A Abbott – Headmaster
1884
Flatterland – Euclidean & Non-Euclidean, Physics
Ian Stewart
2001

29. 5-4 Study Guide Flatland – 0 to 3 dimensions – Euclidean Geometry
Edwin A Abbott – Headmaster
1884
Flatterland – Euclidean & Non-Euclidean, Physics
Ian Stewart
2001

30. 5-4 Practice Flatland – 0 to 3 dimensions – Euclidean Geometry
Edwin A Abbott – Headmaster
1884
Flatterland – Euclidean & Non-Euclidean, Physics
Ian Stewart
2001

31. 5-4 Practice Flatland – 0 to 3 dimensions – Euclidean Geometry
Edwin A Abbott – Headmaster
1884
Flatterland – Euclidean & Non-Euclidean, Physics
Ian Stewart
2001

32. Homework
Study Guide & Practice 5-4
Study Guide & Practice 5-5