Read the proof. Given: m∠H = 30°, m∠J = 50°, m∠P = 50°, m∠N = 100° Prove: △HKJ ~ △LNP Triangles H K J and L N P are shown. Triangle L N P is smaller and to the right of triangle H K J. StatementReason 1. m∠H = 30°, m∠J = 50°, m∠P = 50°, m∠N = 100°1. given 2. m∠H + m∠J + m∠K = 180°2. ? 3. 30° + 50° + m∠K = 180°3. substitution property 4. 80° + m∠K = 180°4. addition 5. m∠K = 100°5. subtraction property of equality 6. m∠J = m∠P; m∠K = m∠N6. substitution 7. ∠J ≅ ∠P; ∠K ≅ ∠N7. if angles are equal then they are congruent 8. △HKJ ~ △LNP8. AA similarity theorem Which reason is missing in step 2? CPCTC definition of supplementary angles triangle parts relationship theorem triangle angle sum theorem

The correct option is;

Triangle angle sum theorem

Step-by-step explanation:

Statement                                                                        Reason

1. m∠H = 30° m∠J = 50°, m∠P = 50° m∠N = 100°           Given

2. ∠H + m∠J + m∠K = 180°                                  (Triangle angle sum theorem)

3. 30° + 50° + m∠K = 180°                                                (Substitution property)

4. 80° + m∠K = 180°                                                          (addition)

5. m∠K = 100°                                                                    (subtraction property)

6. m∠J = m∠P; m∠K = m∠N                                              (substitution)

7. m∠J ≅ m∠P; m∠K ≅ m∠N If angles are equal then they are congruent

8. ΔHKJ ~ ΔLNP      AA similarity theorem.

a)(x-2)^2+(y-1)^2=9

step-by-step explanation:

(picture explains)