Match the reasons with the statements given. given: 1 = 2 5 = 6 prove: mq = mp 1. ∠3, ∠5 are supplementary and ∠4, ∠6 are supplementary exterior sides in opposite rays. 2. ∠5 = ∠6 and ∠1 = ∠2 cpcte 3. ∠3 = ∠4 reflexive 4. mn = mn supplements to = angles. 5. triangle mnq congruent to triangle mnp asa 6. mq = mp given

The answer:

1. ∠3, ∠5 are supplementary and ∠4, ∠6 are supplementary exterior sides in opposite rays.
2. ∠5 = ∠6 and ∠1 = ∠2 cpcte
3. ∠3 = ∠4 reflexive
4. mn = mn supplements to = angles.
5. triangle mnq congruent to triangle mnp asa 6. mq = mp given
the statements given above are true, but for proving   mq = mp, it is sufficient to prove that the triangle mqp is an isosceles.
for that 
∠1 = ∠2, because the line mn bisects ∠m in two similar parts, and 
besides pq and mn are  perpendicular, then it is obvious that mqp is an isosceles triangle.

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