Question

1. given: ∠jkm and ∠mkl form a linear pair; ∠jkm and ∠lkn are supplementary. prove: ∠mkl ≅ ∠lkn. statements reasons 1. ∠jkm and ∠mkl form a linear pair 1. given 2. ∠jkm and ∠mkl are supplementary 2. 3. ∠jkm and ∠lkn are supplementary 3. given 4. ∠mkl ≅ ∠lkn 4.

Explanation:

Step1: Recall linear - pair property

If two angles form a linear pair, they are supplementary. So, since $\angle{JKM}$ and $\angle{MKL}$ form a linear pair, $\angle{JKM}+\angle{MKL}=180^{\circ}$.

Step2: Use given supplementary - angle information

We know that $\angle{JKM}$ and $\angle{LKN}$ are supplementary, so $\angle{JKM}+\angle{LKN}=180^{\circ}$.

Step3: Apply the transitive property of equality

If $\angle{JKM}+\angle{MKL}=180^{\circ}$ and $\angle{JKM}+\angle{LKN}=180^{\circ}$, then $\angle{JKM}+\angle{MKL}=\angle{JKM}+\angle{LKN}$.

Step4: Subtract $\angle{JKM}$ from both sides

By the subtraction property of equality, if $a + b=a + c$, then $b = c$. So, $\angle{MKL}=\angle{LKN}$, and thus $\angle{MKL}\cong\angle{LKN}$.

Answer:

1. If two angles form a linear pair, they are supplementary.
2. Subtraction property of equality.