Count the number of triangles in the figure below.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 8
The figure is a right triangle with a line from the right-angle corner to the long side and a line from the top corner to the middle of the base. 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 (3): ABC, ACD, CDE
Two parts (4): ABD, ADE, AEF, BDF
Four parts (1): ADF
Total \(=3+4+1=8\) triangles.
Why the other options are incorrect
Option (1) 3 — Incorrect. This leaves out both the triangles made of four parts and those made of two parts.
Option (3) 12 — Incorrect. This also counts the 4 sets of three points on one straight line, such as A, B, F, which make no triangle.
Option (4) 7 — Incorrect. This counts only the triangles made of one and of two parts.