Question

the given information to prove that ∠5 ≅ ∠7.
given: ∠6 ≅ ∠8
prove: ∠5 ≅ ∠7
statement
1 ∠6 ≅ ∠8
2 ∠8 ≅ ∠
3 ∠6 ≅ ∠7
reason
given
select
select

Explanation:

Step1: Identify vertical angles

Vertical angles are congruent. $\angle8$ and $\angle7$ are vertical angles. So, $\angle8\cong\angle7$ (Vertical Angles Theorem).

Step2: Use transitive property

Since $\angle6\cong\angle8$ (given) and $\angle8\cong\angle7$, by the transitive property of congruence (if $a = b$ and $b = c$, then $a = c$ for congruent angles), $\angle6\cong\angle7$.

Step3: Identify vertical angles again

$\angle5$ and $\angle6$ are vertical angles. So, $\angle5\cong\angle6$ (Vertical Angles Theorem).

Step4: Use transitive property again

Since $\angle5\cong\angle6$ and $\angle6\cong\angle7$, by the transitive property of congruence, $\angle5\cong\angle7$.

For the table:

• In row 2, the blank should be filled with $7$ (because $\angle8$ and $\angle7$ are vertical angles). The reason is "Vertical Angles Theorem".
• In row 3, the reason is "Transitive Property of Congruence" (using $\angle6\cong\angle8$ (given) and $\angle8\cong\angle7$ (from row 2)).

Answer:

For the table:

• Row 2: Statement is $\angle8\cong\angle7$, Reason is "Vertical Angles Theorem".
• Row 3: Reason is "Transitive Property of Congruence".

And we have proved that $\angle5\cong\angle7$ as shown in the step - by - step explanation.