1. Triangle Inequalities
by: Thess C. Reluba

2. Guess the
Magic Word !

3. Read the question in Column A and click the correct answer in column B
Read the question in Column A and click the correct answer in column B. Each
answer corresponds to a letter or a code.
Place them in the decoder to form the
MAGIC WORD.

4. Column A Column B
1. A polygon with the least number altitude
of sides
bisector
2. A segment drawn from any vertex of the triangle
to the midpoint of the opposite side complementary
3. The longest side in a right triangle hypotenuse
4. The sum of the interior angles of any triangle incenter
5. A triangle with one right angle isosceles triangle
6. It is a triangle with no equal sides legs
7. The point of concurrency of the bisectors median
of the triangle
orthocenter
8. The relation of the acute angles of the right triangle
perpendicular
The height of the triangle
right triangle
10. The relation of the legs of the right triangle
scalene triangle
11. A triangle with 2 equal sides
supplementary
Decoder: triangle
180°
360° E O N I O C S P L O R A S T O B

5. Column A Column B
1. A polygon with the least number altitude
of sides
bisector
2. A segment drawn from any vertex of the triangle
to the midpoint of the opposite side complementary
3. The longest side in a right triangle hypotenuse
4. The sum of the interior angles of any triangle incenter
5. A triangle with one right angle isosceles triangle
6. It is a triangle with no equal sides legs
7. The point of concurrency of the bisectors median
of the triangle
orthocenter
8. The relation of the acute angles of the right triangle
perpendicular
The height of the triangle
right triangle
10. The relation of the legs of the right triangle
scalene triangle
11. A triangle with 2 equal sides
supplementary
Decoder: triangle
180°
360° E O N I O C S P L O R A A S S T T O B

6. Column A Column B
1. A polygon with the least number altitude
of sides
bisector
2. A segment drawn from any vertex of the triangle
to the midpoint of the opposite side complementary
3. The longest side in a right triangle hypotenuse
4. The sum of the interior angles of any triangle incenter
5. A triangle with one right angle isosceles triangle
6. It is a triangle with no equal sides legs
7. The point of concurrency of the bisectors median
of the triangle
orthocenter
8. The relation of the acute angles of the right triangle
perpendicular
The height of the triangle
right triangle
10. The relation of the legs of the right triangle
scalene triangle
11. A triangle with 2 equal sides
supplementary
Decoder: triangle
180°
360° E O N I O C S P L O R A S T P T O B

7. Column A Column B
1. A polygon with the least number altitude
of sides
bisector
2. A segment drawn from any vertex of the triangle
to the midpoint of the opposite side complementary
3. The longest side in a right triangle hypotenuse
4. The sum of the interior angles of any triangle incenter
5. A triangle with one right angle isosceles triangle
6. It is a triangle with no equal sides legs
7. The point of concurrency of the bisectors median
of the triangle
orthocenter
8. The relation of the acute angles of the right triangle
perpendicular
The height of the triangle
right triangle
10. The relation of the legs of the right triangle
scalene triangle
11. A triangle with 2 equal sides
supplementary
Decoder: triangle
180°
360° E O N I O C S P L O R A S T P T I O B

8. E O N I O C S P L O R A S T P T I O O 11 10 7 2 9 5 6 1 3 4 8 B
Column A Column B
1. A polygon with the least number altitude
of sides
bisector
2. A segment drawn from any vertex of the triangle
to the midpoint of the opposite side complementary
3. The longest side in a right triangle hypotenuse
4. The sum of the interior angles of any triangle incenter
5. A triangle with one right angle isosceles triangle
6. It is a triangle with no equal sides legs
7. The point of concurrency of the bisectors median
of the triangle
orthocenter
8. The relation of the acute angles of the right triangle
perpendicular
The height of the triangle
right triangle
10. The relation of the legs of the right triangle
scalene triangle
11. A triangle with 2 equal sides
supplementary
Decoder: triangle
180°
360° E O N I O C S P L O R A S T P T I O O B

9. E O N I O C S P L O R A S T P R T I O O 11 10 7 2 9 5 6 1 3 4 8 B
Column A Column B
1. A polygon with the least number altitude
of sides
bisector
2. A segment drawn from any vertex of the triangle
to the midpoint of the opposite side complementary
3. The longest side in a right triangle hypotenuse
4. The sum of the interior angles of any triangle incenter
5. A triangle with one right angle isosceles triangle
6. It is a triangle with no equal sides legs
7. The point of concurrency of the bisectors median
of the triangle
orthocenter
8. The relation of the acute angles of the right triangle
perpendicular
The height of the triangle
right triangle
10. The relation of the legs of the right triangle
scalene triangle
11. A triangle with 2 equal sides
supplementary
Decoder: triangle
180°
360° E O N I O C S P L O R A S T P R T I O O B

10. E O N I O C S P L O R A S T P R A T I O O 11 10 7 2 9 5 6 1 3 4 8 B
Column A Column B
1. A polygon with the least number altitude
of sides
bisector
2. A segment drawn from any vertex of the triangle
to the midpoint of the opposite side complementary
3. The longest side in a right triangle hypotenuse
4. The sum of the interior angles of any triangle incenter
5. A triangle with one right angle isosceles triangle
6. It is a triangle with no equal sides legs
7. The point of concurrency of the bisectors median
of the triangle
orthocenter
8. The relation of the acute angles of the right triangle
perpendicular
The height of the triangle
right triangle
10. The relation of the legs of the right triangle
scalene triangle
11. A triangle with 2 equal sides
supplementary
Decoder: triangle
180°
360° E O N I O C S P L O R A S T P R A T I O O B

11. E O N I O C S P L O R A S T O P R A T I O O 11 10 7 2 9 5 6 1 3 4 8 B
Column A Column B
1. A polygon with the least number altitude
of sides
bisector
2. A segment drawn from any vertex of the triangle
to the midpoint of the opposite side complementary
3. The longest side in a right triangle hypotenuse
4. The sum of the interior angles of any triangle incenter
5. A triangle with one right angle isosceles triangle
6. It is a triangle with no equal sides legs
7. The point of concurrency of the bisectors median
of the triangle
orthocenter
8. The relation of the acute angles of the right triangle
perpendicular
The height of the triangle
right triangle
10. The relation of the legs of the right triangle
scalene triangle
11. A triangle with 2 equal sides
supplementary
Decoder: triangle
180°
360° E O N I O C S P L O R A S T O P R A T I O O B

12. E O N I O C S P L O R A S T O P R A T I O N O 11 10 7 2 9 5 6 1 3 4 8
Column A Column B
1. A polygon with the least number altitude
of sides
bisector
2. A segment drawn from any vertex of the triangle
to the midpoint of the opposite side complementary
3. The longest side in a right triangle hypotenuse
4. The sum of the interior angles of any triangle incenter
5. A triangle with one right angle isosceles triangle
6. It is a triangle with no equal sides legs
7. The point of concurrency of the bisectors median
of the triangle
orthocenter
8. The relation of the acute angles of the right triangle
perpendicular
The height of the triangle
right triangle
10. The relation of the legs of the right triangle
scalene triangle
11. A triangle with 2 equal sides
supplementary
Decoder: triangle
180°
360° E O N I O C S P L O R A S T O P R A T I O N O B

13. E O N I O C S P L O R A S T O P E R A T I O N O
Column A Column B
1. A polygon with the least number altitude
of sides
bisector
2. A segment drawn from any vertex of the triangle
to the midpoint of the opposite side complementary
3. The longest side in a right triangle hypotenuse
4. The sum of the interior angles of any triangle incenter
5. A triangle with one right angle isosceles triangle
6. It is a triangle with no equal sides legs
7. The point of concurrency of the bisectors median
of the triangle
orthocenter
8. The relation of the acute angles of the right triangle
perpendicular
The height of the triangle
right triangle
10. The relation of the legs of the right triangle
scalene triangle
11. A triangle with 2 equal sides
supplementary
Decoder: triangle
180°
360° E O N I O C S P L O R A S T O P E R A T I O N O B

14. E O N I O C S P L O R A S T O O P E R A T I O N O
Column A Column B
1. A polygon with the least number altitude
of sides
bisector
2. A segment drawn from any vertex of the triangle
to the midpoint of the opposite side complementary
3. The longest side in a right triangle hypotenuse
4. The sum of the interior angles of any triangle incenter
5. A triangle with one right angle isosceles triangle
6. It is a triangle with no equal sides legs
7. The point of concurrency of the bisectors median
of the triangle
orthocenter
8. The relation of the acute angles of the right triangle
perpendicular
The height of the triangle
right triangle
10. The relation of the legs of the right triangle
scalene triangle
11. A triangle with 2 equal sides
supplementary
Decoder: triangle
180°
360° E O N I O C S P L O R A S T O O P E R A T I O N O B

15. E O N I O C S P L O R A S T C O O P E R A T I O N O
Column A Column B
1. A polygon with the least number altitude
of sides
bisector
2. A segment drawn from any vertex of the triangle
to the midpoint of the opposite side complementary
3. The longest side in a right triangle hypotenuse
4. The sum of the interior angles of any triangle incenter
5. A triangle with one right angle isosceles triangle
6. It is a triangle with no equal sides legs
7. The point of concurrency of the bisectors median
of the triangle
orthocenter
8. The relation of the acute angles of the right triangle
perpendicular
The height of the triangle
right triangle
10. The relation of the legs of the right triangle
scalene triangle
11. A triangle with 2 equal sides
supplementary
Decoder: triangle
180°
360° E O N I O C S P L O R A S T C O O P E R A T I O N O B

16. COOPERATION

17. oops sorry!!!

18. oops sorry!!!

19. oops sorry!!!

20. oops sorry!!!

21. oops sorry!!!

22. oops sorry!!!

23. oops sorry!!!

24. oops sorry!!!

25. oops sorry!!!

26. oops sorry!!!

27. oops sorry!!! 10

28. ACTIVITY
# 1

29. Determine if the given combinations/triples can be formed into a triangle by joining the sticks at their endpoints.

30. Can you form a triangle with the ff. triples?
Yes or No
2 , 2 , 3
2 , 3 , 4
5 , 4 , 3
3 , 4 , 7
5 , 5 , 5
7 , 5 , 6
6 , 4 , 2
7 , 2 , 4
3 , 5 , 7
2 , 3 , 6

31. Can you form a triangle with the ff. triples?
Yes or No
2 , 2 , 3
Yes
2 , 3 , 4
5 , 4 , 3
3 , 4 , 7
5 , 5 , 5
7 , 5 , 6
6 , 4 , 2
7 , 2 , 4
3 , 5 , 7
2 , 3 , 6

32. Can you form a triangle with the ff. triples?
Yes or No
2 , 2 , 3
Yes
2 , 3 , 4
5 , 4 , 3
3 , 4 , 7
5 , 5 , 5
7 , 5 , 6
6 , 4 , 2
7 , 2 , 4
3 , 5 , 7
2 , 3 , 6

33. Can you form a triangle with the ff. triples?
Yes or No
2 , 2 , 3
Yes
2 , 3 , 4
5 , 4 , 3
3 , 4 , 7
5 , 5 , 5
7 , 5 , 6
6 , 4 , 2
7 , 2 , 4
3 , 5 , 7
2 , 3 , 6

34. Can you form a triangle with the ff. triples?
Yes or No
2 , 2 , 3
Yes
2 , 3 , 4
5 , 4 , 3
3 , 4 , 7 No
5 , 5 , 5
7 , 5 , 6
6 , 4 , 2
7 , 2 , 4
3 , 5 , 7
2 , 3 , 6

35. Can you form a triangle with the ff. triples?
Yes or No
2 , 2 , 3
Yes
2 , 3 , 4
5 , 4 , 3
3 , 4 , 7 No
5 , 5 , 5
7 , 5 , 6
6 , 4 , 2
7 , 2 , 4
3 , 5 , 7
2 , 3 , 6

36. Can you form a triangle with the ff. triples?
Yes or No
2 , 2 , 3
Yes
2 , 3 , 4
5 , 4 , 3
3 , 4 , 7 No
5 , 5 , 5
7 , 5 , 6
6 , 4 , 2
7 , 2 , 4
3 , 5 , 7
2 , 3 , 6

37. Can you form a triangle with the ff. triples?
Yes or No
2 , 2 , 3
Yes
2 , 3 , 4
5 , 4 , 3
3 , 4 , 7 No
5 , 5 , 5
7 , 5 , 6
6 , 4 , 2
7 , 2 , 4
3 , 5 , 7
2 , 3 , 6

38. Can you form a triangle with the ff. triples?
Yes or No
2 , 2 , 3
Yes
2 , 3 , 4
5 , 4 , 3
3 , 4 , 7 No
5 , 5 , 5
7 , 5 , 6
6 , 4 , 2
7 , 2 , 4
3 , 5 , 7
2 , 3 , 6

39. Can you form a triangle with the ff. triples?
Yes or No
2 , 2 , 3
Yes
2 , 3 , 4
5 , 4 , 3
3 , 4 , 7 No
5 , 5 , 5
7 , 5 , 6
6 , 4 , 2
7 , 2 , 4
3 , 5 , 7
2 , 3 , 6

40. Can you form a triangle with the ff. triples?
Yes or No
2 , 2 , 3
Yes
2 , 3 , 4
5 , 4 , 3
3 , 4 , 7 No
5 , 5 , 5
7 , 5 , 6
6 , 4 , 2
7 , 2 , 4
3 , 5 , 7
2 , 3 , 6

41. Can you form a triangle with the ff. triples?
Yes or No
2 , 2 , 3
Yes
2 , 3 , 4
5 , 4 , 3
3 , 4 , 7 No
5 , 5 , 5
7 , 5 , 6
6 , 4 , 2
7 , 2 , 4
3 , 5 , 7
2 , 3 , 6

42. If you have 2 sticks with lengths 5 cm and 8 cm, what are the possible integral values for the length of the 3rd side?

43. ACTIVITY
# 2

44. Find the range of integral values for the length of the 3rd side and the number of triangles that can be formed

45. 3 and 4 8 and 16 13 and 7 40 and 21 Given Range of possible
length of the 3rd side
# of triangles that
can be formed
3 and 4
8 and 16
13 and 7
40 and 21

46. 3 and 4 1 < 3rd < 7 8 and 16 13 and 7 40 and 21 Given
Range of possible
length of the 3rd side
# of triangles that
can be formed
3 and 4
1 < 3rd < 7
8 and 16
13 and 7
40 and 21

47. 3 and 4 1 < 3rd < 7 5 triangles 8 and 16 13 and 7 40 and 21
Given
Range of possible
length of the 3rd side
# of triangles that
can be formed
3 and 4
1 < 3rd < 7
5 triangles
8 and 16
13 and 7
40 and 21

48. 3 and 4 1 < 3rd < 7 5 triangles 8 and 16 8 < 3rd < 24
Given
Range of possible
length of the 3rd side
# of triangles that
can be formed
3 and 4
1 < 3rd < 7
5 triangles
8 and 16
8 < 3rd < 24
13 and 7
40 and 21

49. 3 and 4 1 < 3rd < 7 5 triangles 8 and 16 8 < 3rd < 24
Given
Range of possible
length of the 3rd side
# of triangles that
can be formed
3 and 4
1 < 3rd < 7
5 triangles
8 and 16
8 < 3rd < 24
15 triangles
13 and 7
40 and 21

50. 3 and 4 1 < 3rd < 7 5 triangles 8 and 16 8 < 3rd < 24
Given
Range of possible
length of the 3rd side
# of triangles that
can be formed
3 and 4
1 < 3rd < 7
5 triangles
8 and 16
8 < 3rd < 24
15 triangles
13 and 7
6 < 3rd < 20
40 and 21

51. 3 and 4 1 < 3rd < 7 6 triangles 8 and 16 8 < 3rd < 24
Given
Range of possible
length of the 3rd side
# of triangles that
can be formed
3 and 4
1 < 3rd < 7
6 triangles
8 and 16
8 < 3rd < 24
16 triangles
13 and 7
6 < 3rd < 20
13 triangles
40 and 21

52. 3 and 4 1 < 3rd < 7 5 triangles 8 and 16 8 < 3rd < 24
Given
Range of possible
length of the 3rd side
# of triangles that
can be formed
3 and 4
1 < 3rd < 7
5 triangles
8 and 16
8 < 3rd < 24
15 triangles
13 and 7
6 < 3rd < 20
13 triangles
40 and 21
19 < 3rd < 61

53. 3 and 4 1 < 3rd < 7 5 triangles 8 and 16 8 < 3rd < 24
Given
Range of possible
length of the 3rd side
# of triangles that
can be formed
3 and 4
1 < 3rd < 7
5 triangles
8 and 16
8 < 3rd < 24
15 triangles
13 and 7
6 < 3rd < 20
13 triangles
40 and 21
19 < 3rd < 61
41 triangles

54. The sum of any two sides must be greater than the third side.
Generalization :
The sum of any two sides must be greater than the third side.

55. The sum of any two sides must be greater than the third side.
Generalization :
The sum of any two sides must be greater than the third side.
The length of third side must be greater than the difference but less than the sum of two sides.

57. Let’s check how well you know.

58. Two sides of a triangle measures 23 m and
7 m. Tell whether or not ( yes or no ) each of the following can be measurement for the 3rd side.
a m
b m
c m
d m
e m

59. 2. If a triangle has 2 sides measuring 9 units
and 7 units, then the measure of the 3rd side
is longer than ___ units and shorter than ___
units.

60. 2. If a triangle has 2 sides measuring 9 units
and 7 units, then the measure of the 3rd side
is longer than ___ units and shorter than ___
units.
3. What is the range of possible integral values
for the length of the third side if the lengths of
two sides of a triangle are 6 and 12 ?

61. 2. If a triangle has 2 sides measuring 9 units
and 7 units, then the measure of the 3rd side
is longer than ___ units and shorter than ___
units.
3. What is the range of possible integral values
for the length of the third side if the lengths of
two sides of a triangle are 6 and 12 ?
4. How many triangles with integral length can you
form if the length of two sides are 15 and 10 ?

62. Time for home activity

63. Find the range of values of the diagonals AC and BD of the quadrilateral below.
2. Find the range of values for
the legs of an isosceles
triangle whose length base…
a. 5 cm
b. 11 m
c. 7 cm