The simplest triangles are ABG, BCG, CGE, CDE, AGE and AEF i.e. 6 in number.
The triangles composed of two components each are ABE, ABC, BCE and ACE i.e. 4 in number.
There are 6 + 4 = 10 triangles in the figure.
The horizontal lines are IJ, AB, EF, MN, HG, DC and LK i.e. 7 in number.
The vertical lines are AD, EH, IL, FG, BC and JK i.e. 6 in number.
Thus, there are 7 + 6 = 13 straight lines in the figure.
The horizontal lines are AK, BJ, CI, DH and EG i.e. 5 in number.
The vertical lines are AE, LF and KG i.e. 3 in number.
The slanting lines are LC, CF, FI, LI, EK and AG i.e. 6 in number.
Thus, there are 5 + 3 + 6 = 14 straight lines in the figure.
The simplest triangles are AFB, FEB, EBC, DEC, DFE and AFD i.e. 6 in number.
The triangles composed of two components each are AEB, FBC, DFC, ADE, DBE and ABD i.e. 6 in number.
The triangles composed of three components each are ADC and ABC i.e. 2 in number.
There is only one triangle i.e. DBC which is composed of four components.
Thus, there are 6 + 6 + 2 + 1 = 15 triangles in the figure.
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