A conjecture and the paragraph proof used to prove the conjecture are shown.
Drag an expression or statement to each box to complete the proof.

It is given that ∠1≅ ∠4 . By the vertical angle theorem, [blank] ≅∠1 . Therefore, ∠2≅∠4 by the substitution property. By the [blank] , ∠4≅∠3 . So, ∠2≅[blank] by the [blank]

choices:
verticle angle theorim, transitive property of congruence, ∠4, ∠3, ∠2, ∠1

∠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."

grantgreving1 grantgreving1 · Answer 2 · 2020-10-14T15:45:07+02:00

grantgreving1 grantgreving1

14-10-2020

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