Question

Show that addition of line segments is commutative up to congruence: Given segments AB, CD, then AB + CD =~ CD + AB.

Answer 1

We are knowing the Commutative Property of addition is a + b = b + a

                                 Commutative Property of multiplication is a X b = b X a

Let us consider 2 distinct segments i.e. seg AB and seg CD

If ' f ' is an element of seg AB such that

Similarly , ,

Now AB + CD = f + g ............... (1)

IF CD + AB = g + f .................. (2)

By Commutative property of addition f + g = g + f ................ (3)

AB + CD = CD + AB .................. (From 1, 2 and 3)

If L.H.S = R.H.S then,

*Dear student you can also prove the commutative property of 2 segments by constructing two segments separately *