Question

∠skf is complementary to ∠fkp
∠fkp is complementary to ∠pkh
prove: ∠skf≅∠pkh
the two - column proof shown includes statements and reasons that are not in the correct order to prove that ∠skf≅∠pkh.

step #	statement	reason

|2|∠skf is complementary to ∠fkp
∠fkp is complementary to ∠pkh|given|

3	∠skf≅∠pkh	definition of congruence
4	m∠skf = m∠pkh	subtraction property of equality

|5|m∠skf + m∠fkp = 90°
m∠fkp + m∠pkh = 90°|definition of complementary angles|
which sequence puts the steps in the correct order to prove that ∠skf≅∠pkh?
1,2,3,5,4
2,5,1,4,3
2,5,4,1,3
5,1,4,2,3

Explanation:

Step1: State given information

We start with the given facts that $\angle SKF$ is complementary to $\angle FKP$ and $\angle FKP$ is complementary to $\angle PKH$. So, the first step should be statement 2.

Step2: Apply definition of complementary angles

Since $\angle SKF$ is complementary to $\angle FKP$ and $\angle FKP$ is complementary to $\angle PKH$, by the definition of complementary angles ($m\angle A + m\angle B=90^{\circ}$ if $\angle A$ and $\angle B$ are complementary), we get $m\angle SKF + m\angle FKP = 90^{\circ}$ and $m\angle FKP + m\angle PKH = 90^{\circ}$, so the second - step is statement 5.

Step3: Use transitive property

Because $m\angle SKF + m\angle FKP = 90^{\circ}$ and $m\angle FKP + m\angle PKH = 90^{\circ}$, we can say $m\angle SKF + m\angle FKP=m\angle FKP + m\angle PKH$ by the transitive property of equality. So, the third - step is statement 1.

Step4: Apply subtraction property of equality

Subtract $m\angle FKP$ from both sides of the equation $m\angle SKF + m\angle FKP=m\angle FKP + m\angle PKH$. We get $m\angle SKF=m\angle PKH$ by the subtraction property of equality. So, the fourth - step is statement 4.

Step5: Use definition of congruence

Since $m\angle SKF=m\angle PKH$, by the definition of congruence (if $m\angle A=m\angle B$, then $\angle A\cong\angle B$), we have $\angle SKF\cong\angle PKH$. So, the fifth - step is statement 3.

Answer:

2,5,1,4,3