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?

Answer 1

Reason: The sum of the interior angles of a triangle is 180° (Triangle Sum Theorem).