Worksheet 2: Getting curious about triangles
Diagram 1 shows a triangle ABC with three given sides [a, b and c] This is Case 1: SSS
c
Diagram 1
Conjecture : A triangle cannot be formed when a + b ≤ c
EXPLORATION 1
Materials used
Drinking straws of lengths of 5cm, 6cm, 7cm, 11cm, 12cm and 15 cm .
Procedure
1. All the possible values of a, b and c that has been chosen from the six lengths of drinking straws are recorded in the Table 1 below.
Length of side
a + b > c
Can a triangle be formed??
a
b
c
7
5
6
Yes
Yes
11
5
7
Yes
Yes
12
5
11
Yes
Yes
15
5
11
Yes
Yes
15
5
12
Yes
Yes
11
6
7
Yes
Yes
12
6
7
Yes
Yes
12
6
11
Yes
Yes
15
6
11
Yes
Yes
15
6
12
Yes
Yes
12
7
11
Yes
Yes
15
7
11
Yes
Yes
15
7
12
Yes
Yes
15
11
12
Yes
Yes
5
6
11
No
No
5
6
12
No
No
5
6
15
No
No
5
7
12
No
No
5
7
15
No
No
6
7
15
No
No
Table 1
2. For each set of values of a, b and c, we used drinking straws of lengths a, b and c to form a triangle. I cannot always form triangles with the lengths used. The records are tabulated in Table 1.
Conclusion
1. Does your finding support your conjecture? Explain your reasoning.
Yes, it did support.
2. State clearly the conclusion that can be drawn from your exploration on the relationship between the lengths of the three sides of a triangle. Prove the relationship.
If a + b ≤ c, then a triangle cannot be formed. If a + b > c, then a triangle can be formed. (PHOTO TO PROVE IT)
Worksheet 3: Getting curious about...