If two lines intersect, prove that the vertically opposite angles are equal.

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Solution

Let $A B$ & $C D$ be two lines

$∠ 1 + ∠ 4 = 180^{\circ}$ (CD is a st. line)

$∠ 4 + ∠ 3 = 180^{\circ}$ (AB is a st. line)

$∠ 1 + ∠ 4 = ∠ 4 + ∠ 3$

$∠ 1 = ∠ 3$ similarly $∠ 2 = ∠ 4$
thus proved

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If two lines intersect, prove that the vertically opposite angles are equal.

Let AB & CD be two lines∠1+∠4=180∘ (CD is a st. line)∠4+∠3=180∘ (AB is a st. line)∠1+∠4=∠4+∠3∠1=∠3 similarly ∠2=∠4thus proved

Let $A B$ & $C D$ be two lines

$∠ 1 + ∠ 4 = 180^{\circ}$ (CD is a st. line)

$∠ 4 + ∠ 3 = 180^{\circ}$ (AB is a st. line)

$∠ 1 + ∠ 4 = ∠ 4 + ∠ 3$

$∠ 1 = ∠ 3$ similarly $∠ 2 = ∠ 4$
thus proved