Prove proportions or angle congruences using similarity

[blackdog]

Hello. I have this. How do I prove this? Thank you.

 

[BigBeachBanana]

There are different ways to prove it. What are the options in the dropdown list?

 

[Dumbass]

Hello. I have this. How do I prove this? Thank you.
View attachment 30653

There many ways to prove it.
Did your teacher told you to do your homework in a specific manner

 

[blackdog]

There are different ways to prove it. What are the options in the dropdown list?

The options in the dropdown list are:

AA similarity
Acute angles in a right triangle sum to 90 degrees
Additive property of length
Algebra
All right angles are congruent
Alternate Interior angles theorem
Angles forming a linear pair sum to 180 degrees
Corresponding angles theorem
Definition of similarity
Definition of supplementary angles
Given
Reflexive property of congruence
Reflexive property of equality
SAS similarity
Substitution
Transitive property of congruence
transitive property of equality
vertical angle theorem

The question changed because this is just practice on IXL and the form resubmitted, but I just want to understand better on how to do this.
And where is the best place I can learn?

 

[blackdog]

There many ways to prove it.
Did your teacher told you to do your homework in a specific manner

My teacher just assigns 20 practice questions on IXL, teacher doesnt assign anything in specific you just choose.
I want to learn how to prove these so I can get past my assignment.