Question

Consider the following triangle.
PG,UL, and EA are all medians of A ALG, and C is the centroid.
Which of the following statements IS NOT true?

Answer 1

Answer: C

Step-by-step explanation:

U have to add the numbers up. Then times it by 2/3 and 1/3 to see if the same numbers are on ur screen.

Answer 2

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)

• Plug in the value of 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)

• Plug in the value of CE

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)

• Plug in the value of CL

5 = 2/3(UL)

3 × 5 = 2(UL)

15 = 2(UL)

15/2 = UL

UL = 7.5

CU = 1/3(UL)

• Plug in the value of 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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