Question

complete the following proof by filling in the blanks. given: ∠1≅∠a prove: ∠1≅∠6 statements reasons 1) ∠1≅∠a 1) given 2) ∠a≅∠6 2) 7 3) 7 3) transitive property of congruence 4) ∠1≅∠1 4) 7 5) ∠1≅∠6 5) 7 statements reasons 1) ∠1≅∠a 1) given 2) ∠a≅∠6 2) 3) 3) transitive property of congruence 4) ∠1≅∠1 4) help me solve this view an example get more help.

Explanation:

Step1: Identify vertical - angle congruence

$\angle A\cong\angle 6$ because vertical angles are congruent.

Step2: Apply transitive property

Since $\angle 1\cong\angle A$ (given) and $\angle A\cong\angle 6$, by the transitive property of congruence, $\angle 1\cong\angle 6$.

Step3: Identify reflexive property

$\angle 1\cong\angle 1$ by the reflexive property of congruence.

Answer:

1. Vertical angles are congruent; 3) $\angle 1\cong\angle 6$; 4) Reflexive property of congruence; 5) Transitive property of congruence (using $\angle 1\cong\angle A$, $\angle A\cong\angle 6$)