Question

In the given figure,angle 1=angle 2,angle 3=angle4.Show that angle ABC= angle DBC. State the euclid's 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

Concept:

From Euclid’s second axiom, we will use this one "If equals be added to equals, the wholes are equal" to answer the given question.

Given:

∠1 = ∠2

∠3 = ∠4

Find:

∠ABC = ∠DBC

Solution:

We know ∠3 = ∠4

let's add ∠x on both side

∠3 + ∠x = ∠4 + ∠x

let's ∠x = ∠1, substituting value of x

∠3 + ∠1 = ∠4 + ∠1

we also know, ∠1 = ∠2

Substituting the value of ∠1 we can write the equation as,

∠3 + ∠1 = ∠4 + ∠2

which is nothing but

∠ABC = ∠DBC

Hence ∠ABC = ∠DBC

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