Question

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

Explanation:

Step1: Identify vertical - angle property

Vertical angles are congruent. Since $\angle3$ and $\angle6$ are vertical angles, $\angle3\cong\angle6$. So, a. is "Vertical angles are congruent".

Step2: Apply transitive property

From $\angle1\cong\angle3$ and $\angle3\cong\angle6$, by the transitive property of congruence, we get $\angle1\cong\angle6$. So, b. is "$\angle1\cong\angle6$".

Step3: Identify vertical - angle property again

Since $\angle1$ and $\angle4$ are vertical angles, $\angle1\cong\angle4$. So, c. is "Vertical angles are congruent".

Step4: Apply transitive property again

From $\angle1\cong\angle6$ and $\angle1\cong\angle4$, by the transitive property of congruence, we get $\angle6\cong\angle4$. So, d. is "Transitive Property of Congruence".

Answer:

a. Vertical angles are congruent
b. $\angle1\cong\angle6$
c. Vertical angles are congruent
d. Transitive Property of Congruence