1. GEOMETRY 5.5
INEQUALITIES involving 2 Triangles
Pages: 273 – 275
Objectives:
Learn and use the SAS Inequality Theorem
Learn and use the SSS Inequality Theorem

2. GEOMETRY 5.5
SAS Inequality Theorem (Hinge) IF
Two Sides of One Triangle are CONGRUENT,
respectively, to Two Sides of a Second Triangle
AND
the INCLUDED Angle of the First Triangle is
GREATER Than the INCLUDED angle of the Second,
THEN
The THIRD Side of the First Triangle is LONGER than
the Third Side of the Second Triangle.

3. F
GEOMETRY 5.5 E C A B D
Given:
Prove: AB > DE

4. GEOMETRY 5.5 U T 50 10 10
100 20 8 8 Y W X
YU _______ XT

5. GEOMETRY 5.5
SSS Inequality Theorem
IF -- Two SIDES of One Triangle are CONGRUENT,
respectively, to Two Sides of a Second Triangle,
AND
the LENGTH of the Third Side of the First Triangle
is GREATER than the Length of the Third Side of
the Second Triangle
THEN -- The ANGLE Opposite the Third Side of the
First Triangle is GREATER than the
Angle Opposite the Third Side of the Second
Triangle.

6. GEOMETRY 5.5 D C 2 1 A B
Given:
Prove:

7. GEOMETRY 5.5 D 2 1 B C A
Given:
Prove:

8. P Q R 1 2
Given: S
Prove:

9. GEOMETRY 5.5 S 4 3 1 2 R Q P

10. GEOMETRY 5.5 S 4 3 1 2 R Q P

11. GEOMETRY 5.5 S 4 3 1 2 R Q P

12. GEOMETRY 5.5

13. GEOMETRY 5.5

14. GEOMETRY 5.5

15. GEOMETRY 5.5 L

16. GEOMETRY 5.5

17. GEOMETRY 5.5

18. GEOMETRY 5.5

19. GEOMETRY 5.5

20. GEOMETRY 5.5

21. GEOMETRY 5.5

22. GEOMETRY 5.5

23. GEOMETRY 5.5

24. GEOMETRY 5.5
Sometimes True
Always True, or
Never True?
The Lengths of Two Sides of a Triangle are EQUAL,
respectively, to the Lengths of Two sides of a Second
Triangle,
and the Third Side of the First Triangle is Longer
than the Third Side of the Second Triangle.

25. GEOMETRY 5.5
GEOMETRY 5.5
Sometimes True
Always True, or
Never True?
The Lengths of Two Sides of a Triangle are EQUAL,
respectively, to the Lengths of Two sides of a Second
Triangle,
and the Third Side of the First Triangle is Longer
than the Third Side of the Second Triangle.
Sometimes True

26. GEOMETRY 5.5
Sometimes True
Always True, or
Never True?
The Lengths of Two Sides of a Triangle are EQUAL,
respectively, to the Lengths of Two Sides of a Second
Triangle,
the INCLUDED angle of the First Triangle is GREATER
than the Included Angle of the Second Triangle,
and the Third Sides are EQUAL in Length.

27. GEOMETRY 5.5
Sometimes True
Always True, or
Never True?
The Lengths of Two Sides of a Triangle are EQUAL,
respectively, to the Lengths of Two Sides of a Second
Triangle,
the INCLUDED angle of the First Triangle is GREATER
than the Included Angle of the Second Triangle,
and the Third Sides are EQUAL in Length.
Never True

28. GEOMETRY 5.5
Sometimes True
Always True, or
Never True?
The Legs of a Right Triangle are CONGRUENT,
respectively, to the Legs of a Second Right Triangle,
and the Hypotenuse of the First Right Triangle is
LONGER than the Hypotenuse of the Second Right
Triangle.

29. GEOMETRY 5.5
Sometimes True
Always True, or
Never True?
The Legs of a Right Triangle are CONGRUENT,
respectively, to the Legs of a Second Right Triangle,
and the Hypotenuse of the First Right Triangle is
LONGER than the Hypotenuse of the Second Right
Triangle.
Never True

30. P
GEOMETRY 5.5 C D Q

31. GEOMETRY 5.5
You should be able to:
State and use the SAS Inequality Theorem
State and use the SSS Inequality Theorem
Use the SAS and SSS Inequality Theorems in proofs
Use the Inequality Theorems with the Biggest Angle –
Longest Side Theorems to solve problems

32. GEOMETRY 5.5
Write a two-column proof.
Given:
Prove:

33. GEOMETRY 5.5
Given:
Prove:

34. A. Write an inequality relating mLDM to mMDN using the information in the figure.

35. A. Compare mWYX and mZYW and write an inequality statement.
A. mWYX < mZYW
B. mWYX = mZYW
C. mWYX > mZYW
D. cannot be determined
Lesson 5 CYP3

36. B. Find the range of values containing n and write an inequality statement.
Lesson 5 CYP3