Question

complete the following proof by filling in the blanks. given: ∠2≅∠4 prove: ∠6≅∠8 statements reasons 1) ∠2≅∠4 1) given 2) ∠4≅∠8 2) ? 3) ? 3) transitive property of congruence 4) ∠6≅∠2 4) ? 5) ∠6≅∠8 5) ? statements reasons 1) ∠2≅∠4 1) given 2) ∠4≅∠8 2) 3) 3) transitive property of congruence 4) ∠6≅∠2 4) 5) ∠6≅∠8 5)

Explanation:

Step1: Identify vertical - angle property

Vertical angles are congruent. $\angle4$ and $\angle8$ are vertical angles, so $\angle4\cong\angle8$.

Step2: Apply transitive property

Since $\angle2\cong\angle4$ and $\angle4\cong\angle8$, by the transitive property of congruence, $\angle2\cong\angle8$.

Step3: Identify vertical - angle property again

$\angle6$ and $\angle2$ are vertical angles. Vertical angles are congruent, so $\angle6\cong\angle2$.

Step4: Apply transitive property again

Since $\angle6\cong\angle2$ and $\angle2\cong\angle8$, by the transitive property of congruence, $\angle6\cong\angle8$.

Answer:

1. Vertical angles are congruent; 3) $\angle2\cong\angle8$; 4) Vertical angles are congruent; 5) Transitive property of congruence