Question

Suppose it is already stated that ∠6≅∠7 and ∠7≅∠8. What property of congruence justifies the conclusion that ∠6≅∠8.

Short answer

Thetransitive property of congruence justifies∠6≅∠8.

Step-by-step solution

Step 1. State the formula to be used.

According to transitive property of congruence, two things (side or angle) that are equal to the same thing (side or angle) are congruent to each other. That is if $a\cong b$, $b\cong c$, then $a\cong c$.

Step 2. Show the proof.

Here,

$\angle 6\cong \angle 7$ … (i)

$\angle 7\cong \angle 8$ … (ii)

According to the transitive property of congruence, two things that are equal to the same thing(side or angle) are congruent to each other.

From equation (i) and (ii),∠6,∠8are congruent to the angle∠7.

So,$\angle 6\cong \angle 8$

Step 3. State the conclusion.

Therefore, using the transitive property of congruence, $\angle 6\cong \angle 8$.