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? cpctc definition of supplementary angles triangle parts relationship theorem triangle angle sum theorem

Step-by-step explanation:

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

To prove: △HKJ ~ △LNP

Proof:

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

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

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

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

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

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

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

Step 8. △HKJ ~ △LNP( AA similarity theorem)

Hence proved.

Thus, the missing step in 2 is (Triangle angle sum theorem)

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

c

step-by-step explanation: