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)?

Explanation:

Step1: Identify given information

Given $\angle1\cong\angle6$ and $\angle6\cong\angle3$.

Step2: Apply transitive property

Since $\angle1\cong\angle6$ and $\angle6\cong\angle3$, by the transitive - property of congruence, $\angle1\cong\angle3$.

Step3: Given another congruence

Given $\angle4\cong\angle1$.

Step4: Apply transitive property again

Since $\angle4\cong\angle1$ and $\angle1\cong\angle3$, by the transitive - property of congruence, $\angle4\cong\angle3$.

Answer:

1. $\angle1\cong\angle3$; 4) Given; 5) Transitive property of congruence