Analytical Reasoning Questions

A line is an undefined term because of it :

1. Contains an infinite number of points

2. can be used to create other geometric shapes

3. is a term that does not have a formal definition

In Geometry, unless it's stated, a line will extend in one dimension and goes on forever in both ways.

This would not mean that K and L will always be together. It just implies that, if K is there, then L will also be there.

At the same time, it can happen that L is there but K isn't.

Remember, the condition is on K, not on L.

The figure may be labelled as shown

The simplest triangles are ABJ, ACJ, BDH, DHF, CIE and GIE i.e 6 in number.

The triangles composed of two components each are ABC, BDF, CEG, BHJ, JHK, JKI and CJI i.e 7 in number.

There is only one triangle JHI which is composed of four components.

Thus, there are 6 + 7 + 1 = 14 triangles in the given figure.

The horizontal lines are IK, AB, HG and DC i.e. 4 in number.

The vertical lines are AD, EH, JM, FG and BC i.e. 5 in number.

The slanting lines are IE, JE, JF, KF, DE, DH, FC and GC i.e. 8 is number.

Thus, there are 4 + 5 + 8 = 17 straight lines in the figure.

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 simplest rectangles are AEHG, EFJH, FBKJ, JKCL and GILD i.e 5 in number.

The rectangles composed of two components each are AFJG and FBCL i.e 2 in number

Only one rectangle namely AFLD is composed of three components and only one rectangle namely ABCD is composed of five components.

Thus, there are 5 + 2 + 1 + 1 = 9 rectangles in the given 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 simplest triangles are AFJ, FJK, FKB, BKG, JKG, JGC, HJC, HIJ, DIH, DEI, EIJ and AEJ i.e. 12 in number.

The triangles composed of two components each are JFB, FBG, BJG, JFG, DEJ, EJH, DJH and DEH i.e. 8 in number.

The triangles composed of three components each are AJB, JBC, DJC and ADJ i.e. 4 in number.

The triangles composed of six components each are DAB, ABC, BCD and ADC i.e. 4 in number.

Thus, there are 12 + 8 + 4 + 4 = 28 triangles in the figure.