If C is the centroid of ΔALG, considering the centroid theorem of a triangle, the statement that is NOT true is: C. If CE = 0.75 cm, then AC = 2.5 cm.
Based on the centroid theorem of a triangle, the medians of ΔALG all intersect at a concurrent point, C, such that:
- CL = 2/3(UL); CU = 1/3(UL)
- AC = 2/3(AE); CE = 1/3(AE)
- CG = 2/3(PG); CP = 1/3(PG)
Thus, statement 1 would be true because at C, PG, UL, and EA are concurrent.
Statement 2 would be true.
Rationale: If PG = 3 cm, then CG would be,
CG = 2/3(PG)
CG = 2/3(3)
CG = 2 cm
Statement 3 is NOT true.
Rationale: If CE = 0.75 cm, then AC would be,
CE = 1/3(AE)
0.75 = 1/3(AE)
3 × 0.75 = AE
AE = 2.25 cm
Statement 4 is true.
Rationale: If CL = 5 cm, then UC would be,
CL = 2/3(UL)
5 = 2/3(UL)
3 × 5 = 2(UL)
15 = 2(UL)
15/2 = UL
UL = 7.5
CU = 1/3(UL)
CU = 1/3(7.5)
CU = 2.5 cm
In conclusion, if C is the centroid of ΔALG, considering the centroid theorem of a triangle, the statement that is NOT true is: C. If CE = 0.75 cm, then AC = 2.5 cm.
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