Question

A conjecture and the paragraph proof used to prove the conjecture are shown.

Answer 1

Answer:

I did the quiz here is what I got:

Answer 2

Answer:

∠2; vertical angle theorem; ∠3; transitive property of congruence

Step-by-step explanation:

∠2 and ∠1 are opposite angles that share only a vertex.  This is the definition of vertical angles, and by the vertical angle theorem they are congruent.

Substituting ∠2 for ∠1 in our "given" statement, we now know that ∠2≅∠4.

∠4 and ∠3 are opposite angles that share a vertex.  This makes them vertical angles, and the vertical angle theorem states that they are congruent.

The transitive property, algebraically, states "if a=b and b=c, then a=c."  Applied to this proof, it states "if ∠2≅∠4, and ∠4≅∠3, then ∠2≅∠3."