When writing a geometric proof, which angle relationship could be used alone to justify that two angles are congruent?

Vertical angles are always congruent.

Step-by-step explanation:

Vertical angles are always congruent, but congruent angles do not have to be vertical. Any two angles with the same angle measurement are considered congruent by definition.

Imagine (or draw):

an X forming 2 pairs of vertical angles. ∠1 is to the left, ∠2 is on top, ∠3 is to the right, and ∠4 is on the bottom. Vertical angles are always congruent because ∠1 and ∠2 are supplementary, meaning that their measures add to 180 degrees. The measures of ∠2 and ∠3 also add to 180 degrees. This means that:

m∠1+m∠2=180 and m∠2+m∠3=180.

Using the Transitive Property, it becomes m∠1+m∠2=m∠2+m∠3.

If you subtract the measure of ∠2 from both sides,

it becomes m∠1=m∠3

introduction, methodology, results, discussion

step-by-step explanation:

an observational study is one which consists of actual observation to record data and then analyse the data.

there are a number of factors that should be analyzed before starting an observational study.

the main four factors are:

i) introduction:   this should be analysed to check whether the purpose of the study is correctly established and the data recorded are appropriate for the study

methodology:   the method of collecting the data, such as whether randomly selected, and whether sample size matches with the population to be studied, whether questions asked are easy to answer by common men, etc.

results: then results such as summary of data with comments should be studied thoroughly

discussion:   the last is the discussion, this can be either by management people or persons who are all interested , etc.

c.

step-by-step explanation: