Question

Read the proof. Given: m∠H = 30°, m∠J = 50°, m∠P = 50°, m∠N = 100° Prove: △HKJ ~ △LNP 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

B

Explanation:

Answer 2

`2. m\angle H+m\angle J +m\angle K =180^(\circ)`

Reason: the sum of all interior angles of any triangle is equal to 180º.

Explanation:

1) Organizing

Statement 1. m∠H = 30°, m∠J = 50°, m∠P = 50°, m∠N = 100° 1. Reason: given

2) Since the sum of all internal angles of any triangle is equal to 180º, just like the formula. N the number of sides of a triangle:

`S_(i)=180^(\circ)(n-2)\rightarrow 180(3-2) \therefore S_(i)=180^(\circ)`

3) We can also say

`m\angle K=180^(\circ)-(m\angle H+m\angle J)\\m\angle K=180^(\circ)-\left ( 30^(\circ)+50^(\circ) \right )\\m\angle K=100^(\circ)`

Similarly to the other triangle:

`m\angle L=180^(\circ)-(m\angle N+m\angle P)\\m\angle L=180^(\circ)-\left ( 100^(\circ)+50^(\circ) \right )\\m\angle L=30^(\circ)`

4) Hence,

`2. m\angle H+m\angle J +m\angle K =180`

Reason: The sum of interior angles is equal to 180º.