Question

angle 1= angle 3 and angle 2 = angle 4 using euclid axiom show that angle A= angle C state the axiom used

Answer 1

<1=<2  
<3=<4
Adding <1 to both angles
<3+<1 = <4+<1
As mentioned above, <1=<2
Therefore, <3+<1=<2+<4
Which means: <ABC = <DBC

The Euclid's axiom used here is: "If equals are added to equals, the wholes are equal."

Answer 2

<1 = <3

<2=<4

By using Euclid's 6th axiom : '' things which are doubled of the same things are equal to one another.''

<1+<2=<3+<4

<A=<C

Hence, proved by using Euclid's 6th axiom

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