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Georgia [21]
3 years ago
5

Vertical angles are congruent is that an example of a theorem

Mathematics
2 answers:
NISA [10]3 years ago
7 0
Whats the answers? I need them first


Pachacha [2.7K]3 years ago
3 0

Proof:

<span><span>∠1and∠2</span><span>∠1and∠2</span></span> form a linear pair, so by the Supplement Postulate, they are supplementary. That is,

<span><span>m∠1+m∠2=180°</span><span>m∠1+m∠2=180°</span></span>.

<span><span>∠2and∠3</span><span>∠2and∠3</span></span> form a linear pair also, so

<span><span>m∠2+m∠3=180°</span><span>m∠2+m∠3=180°</span></span>.

Subtracting <span><span>m∠2</span><span>m∠2</span></span> from both sides of both equations, we get

<span><span>m∠1=180°−m∠2=m∠3</span><span>m∠1=180°−m∠2=m∠3</span></span>.

Therefore,

<span><span>∠1≅∠3</span><span>∠1≅∠3</span></span>.

You can use a similar argument to prove that <span><span>∠2≅∠4</span><span>∠2≅∠4</span></span>.In the figure, 

<span><span>∠1≅∠3</span><span>∠1≅∠3</span></span> and <span><span>∠2≅∠4</span><span>∠2≅∠4</span></span>.

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