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Mathematics and Life 104 You know maths - Properties of Parallel lines

 You know maths - Properties of Parallel lines


Background Today we will discuss some properties of Parallel lines


The figure below has 7 distinct diagrams numbered one to seven. 



Although many academicians do not like the idea of denoting angles by numbers, I find it very convenient to explain without going into naming angles in terms of vertex, arms. I have also used a,b etc to show different angles.


Figure 1 line l is parallel to m and m is parallel to l. This is called symmetry property.

Figure 2 Line p is parallel to q, p is also parallel to r, so q is parallel to r. This is called transitivity.

Figure 3 line m is parallel to n, p crossing them is called thetransversal. The angles shown as 1 and 2 are called corresponding angles. Because each is above the line. If both angles are below the line, they too are corresponding angles. They are equal.

Figure 4 Line l is parallel to m, q is the transversal. Angles 1 and 2 are called alternate interior angles because they are on alternate sides of the transversal and are in the interior of the parallel lines. They are equal.

Figure 5 Line p is parallel to q, m is the transversal. The angles shown as a and b are called co interior or consecutive interior angles as they are in the interior and are one after the other. They are supplementary or add up to 180 degree.

Figure 6 Lines m, n, p are parallel. a and b are the intercepts. If b makes equal intercepts, so will a. This is known as the equal intercept theorem.

Figure 7 This is in fact a quiz. The lines l, m and n are parallel. Line p is the transversal. I have numbered all possible angles from 1 to 12 in order. The quiz is to write different pairs (or triplets of angles if you can), which are 1. Equal and 2. Supplementary. But you also need to tell the logic or name the property. Like corresponding angles, co interior angles etc.


Answers tomorrow.


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