Question

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

Explanation:

Step1: Recall the transitive - property of congruence

The transitive property of congruence states that if $\angle a\cong\angle b$ and $\angle b\cong\angle c$, then $\angle a\cong\angle c$.

Step2: Identify the given congruences

We are given $\angle1\cong\angle6$ and $\angle6\cong\angle3$. By the transitive property of congruence, we can conclude that $\angle1\cong\angle3$.

Step3: Use the other given congruence

We are also given $\angle4\cong\angle1$. Since $\angle1\cong\angle3$, by the transitive property of congruence again, we can conclude that $\angle4\cong\angle3$.

Answer:

Statements:
(1) $\angle1\cong\angle6$ (Given)
(2) $\angle6\cong\angle3$ (Given)
(3) $\angle1\cong\angle3$ (Transitive property of congruence)
(4) $\angle4\cong\angle1$ (Given)
(5) $\angle4\cong\angle3$ (Transitive property of congruence)

Reasons:
(1) Given
(2) Given
(3) Transitive property of congruence
(4) Given
(5) Transitive property of congruence