Question

Find the number of straight lines and the number of triangles in the complex figure given below.

Answer 1

Usually vertices are not marked, but we can mark to make the counting easy. Number of straight lines are: AB, Be, CD, DA, AC, BD, EH, AH, DH So there are 9 straight lines in the diagram. Now count triangles: Number of small triangles are (containing one component)
AGH, GHD, AFG, DGF, FBE and FCE = 6 Number of triangles with two components: AHF, DHF, AHD, AFD, AFB, DFC, FBC = 7 Number of triangles with four components: ABC, ADC, CDB and ADB = 4
∴∴ Total number of triangles contained in the figure = 6 + 7 + 4= 17
Straight lines = 9
Triangles = 17