Question

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. Statement Reason 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∠N 6. substitution 7. ∠J ≅ ∠P; ∠K ≅ ∠N 7. if angles are equal then they are congruent 8. △HKJ ~ △LNP 8. AA similarity theorem Which reason is missing in step 2? CPCTC definition of supplementary angles triangle parts relationship theorem triangle angle sum theorem

Answer 1

Triangle angle sum theorem

Explanation:

Answer 2

The correct option is;

Triangle angle sum theorem

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.