Question

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

Explanation:

Step1: Identify vertical - angle congruence

Vertical angles are congruent, so $\angle4\cong\angle5$ because vertical angles have equal measures.

Step2: Use transitive property

Since $\angle1\cong\angle4$ and $\angle4\cong\angle5$, by the transitive property of congruence, $\angle1\cong\angle5$.

Step3: Identify vertical - angle congruence again

$\angle1\cong\angle3$ because they are vertical angles.

Step4: Use transitive property again

Since $\angle1\cong\angle5$ and $\angle1\cong\angle3$, by the transitive property of congruence, $\angle3\cong\angle5$.

Answer:

1. Vertical angles are congruent.
2. $\angle1\cong\angle5$
3. Vertical angles are congruent.
4. Transitive property of congruence.