Question

15. In triangle ∆PQR, C is the centroid.

a. If CY = 10, find PC and PY

b. If QC = 10, find ZC and ZQ

c. If PX = 20, find PQ

Answer 1

Because C is the centroid, therefore:

Segments PZ = ZR; RY = YQ; QX = XP

A.
If CY = 10, then

PC = 2*CY = 20
PY = PC + CY = 20 + 10 = 30
Answer: PC = 20 PY = 30

B.
If QC = 10, then

ZC = QC/2 = 5
ZQ = ZC + QC = 5 + 10 = 15
Answer: ZC = 5 ZQ = 15

C.
If PX = 20
Because the median RX bisects side PQ, therefore PX = QX = 20
PQ = PX + QX = 40
Answer: PQ = 40