Find the number of triangles in the figure:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 18
Every triangle in the figure has its three sides on three of its straight lines, so naming the points and counting group by group makes sure none is missed or counted twice. P and Q are the points where MD and ME cross FG.
With the top corner A (3): ADE, AFG, ABC
With M and two points on side AB (3): MBF, MBD, MFD
With M and two points on side AC (3): MCG, MCE, MGE
With M and two points on FG (6): MFP, MFQ, MFG, MPQ, MPG, MQG
With M and DE (1): MDE
Small triangles just above FG (2): DFP, EGQ
Total \(=3+3+3+6+1+2=18\) triangles.