Question
In the we have $\angle1=\angle3$ and $\angle2=\angle4.$ Show that $\angle\text{A}=\angle\text{C}.$
✓
Answer
We have $\angle1=\angle3\ ...(\text{i})$ [Given]
And $\angle2=\angle4\ ...(\text{ii})$ [Given]
Now, by Euclid's axiom 2, we have if equal are added to equals, the whole are equal.
Adding (i) and (ii) we get
$\angle1+\angle2=\angle3+\angle4$
Hence, $\angle\text{A}=\angle\text{C}$
And $\angle2=\angle4\ ...(\text{ii})$ [Given]
Now, by Euclid's axiom 2, we have if equal are added to equals, the whole are equal.
Adding (i) and (ii) we get
$\angle1+\angle2=\angle3+\angle4$
Hence, $\angle\text{A}=\angle\text{C}$
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