Count the number of triangles in the figure below.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 12
The figure is a rectangle with both diagonals and a vertical line through the middle. A triangle is counted when all three of its sides lie on lines of the figure. Naming the corners and crossing points and counting by the number of small parts each triangle covers makes sure none is missed or counted twice.
One part (6): ABD, ADE, BCD, CDG, DEF, DFG
Two parts (2): ACD, DEG
Three parts (4): ACE, ACG, AEG, CEG
Total \(=6+2+4=12\) triangles.
Why the other options are incorrect
Option (2) 17 — Incorrect. This also counts the 5 sets of three points on one straight line, such as A, B, C, which make no triangle.
Option (3) 10 — Incorrect. This leaves out the 2 triangles made of two parts, such as ACD.
Option (4) 8 — Incorrect. This counts only the triangles made of one and of two parts.