Question

Given: angle 2 and angle 4 are vertical. Prove angle 2 congruent to angle 4

Answer 1

Answer:

Refer to pics

Step-by-step explanation:

Answer 2

Vertical angles are two angles which are vertically opposite and have the same measure. Thus, the two angles are to be congruent.

Vertical angles are often formed when two straight lines intersect at a point.

From the given question, the steps to prove that angle 2 and angle 4 are congruent are:

With reference to the sketch attached to this answer;

<AOC + <AOD + <BOC + <BOD = $360^{o}$ (sum of angle at a point)

Thus,

<AOC + <AOD = $180^{o}$ (supplementary angle property)

also,

<BOC + BOD = $180^{o}$ (supplementary angle property)

So that;

<AOD ≅ <BOC (vertically opposite angle property)

Therefore,

<2 and <4 are congruent (vertically opposite angle property)

It can be concluded that vertically opposite angles are equal in measure, thus congruent.

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