Question

match each statement to its correct numbered spot in the proof. given: ∠b≅∠m, (overline{bc}congoverline{mk}). prove: (\triangle abccong\triangle amk). 1. ∠b≅∠m 2 3 4 given 5 6 1 (overline{bc}congoverline{mk}) 2 ∠bac≅∠mak 3 vertical angles 4 aas≅theorem 5 given 6 (\triangle abccong\triangle amk)

Explanation:

Step1: Identify given side - congruence

$\overline{BC}\cong\overline{MK}$ is given, so it should be placed in spot 2.

Step2: Identify vertical - angle congruence

$\angle BAC\cong\angle MAK$ because they are vertical angles. So "Vertical Angles" (which implies $\angle BAC\cong\angle MAK$) should be placed in spot 3 and $\angle BAC\cong\angle MAK$ in spot 4.

Step3: Determine congruence theorem

We have two angles ($\angle B\cong\angle M$ and $\angle BAC\cong\angle MAK$) and a non - included side ($\overline{BC}\cong\overline{MK}$) congruent. By the AAS (Angle - Angle - Side) congruence theorem, $\triangle ABC\cong\triangle AMK$. So "AAS $\cong$ Theorem" should be placed in spot 5 and $\triangle ABC\cong\triangle AMK$ in spot 6.

Answer:

1. $\angle B\cong\angle M$
2. $\overline{BC}\cong\overline{MK}$
3. Vertical Angles
4. $\angle BAC\cong\angle MAK$
5. AAS $\cong$ Theorem
6. $\triangle ABC\cong\triangle AMK$