Given M is the midpoint of segment AB. A proof states AM = MB. What reason justifies that step?

Ray BD bisects angle ABC. The proof writes m<ABD = m<DBC. What reason licenses this line?

Line k bisects segment PQ at R. The proof's next line is PR = RQ. Which reason is needed?

A proof has AB ≅ CD and then writes AB = CD. What reason justifies changing congruent segments to equal lengths?

A proof has angle JKL ≅ angle MNP and then writes m<JKL = m<MNP. What reason supports the step?

Lines r and s are perpendicular at E. A proof states angle 1 is a right angle. What reason justifies this statement?

Angles 1 and 2 are complementary. The proof states m<1 + m<2 = 90°. Which reason justifies the equation?

In triangle ABC, point D is the midpoint of BC. The proof states AD is a median of triangle ABC. What reason justifies the step?

Point B lies between A and C on segment AC. The proof writes AB + BC = AC. What reason justifies this equation?

Ray QS lies inside angle PQR. A proof says m<PQS + m<SQR = m<PQR. Which reason justifies the step?

Angles 4 and 5 form a linear pair. The proof states they are supplementary. What reason should be written?

Lines m and n are parallel, and transversal t makes angle 1 and angle 5 corresponding. The proof states angle 1 ≅ angle 5. What reason fits?

AB ≅ DE, BC ≅ EF, and AC ≅ DF. The proof concludes triangle ABC ≅ triangle DEF. Which reason justifies the conclusion?

AB ≅ DE, AC ≅ DF, and included angle A ≅ included angle D. The proof concludes triangle ABC ≅ triangle DEF. Which reason applies?

Angle A ≅ angle D, AB ≅ DE, and angle B ≅ angle E. The proof concludes triangle ABC ≅ triangle DEF. What reason justifies it?

Point P is not on line q. A proof says there is exactly one line through P parallel to q. Which postulate justifies this?

Lines a and b intersect. Angles 1 and 3 are vertical angles, and the proof states angle 1 ≅ angle 3. What reason justifies it?

Parallel lines r and s are cut by a transversal. Angles 4 and 6 are alternate interior angles, and the proof states angle 4 ≅ angle 6. What reason fits?

Parallel lines p and q are cut by a transversal. Angles 3 and 6 are same-side interior angles, and the proof states they are supplementary. Which reason applies?

For triangle ABC, a proof writes m<A + m<B + m<C = 180°. What theorem justifies this step?

In triangle ABC, side BC is extended through C to D. The proof states m<ACD = m<A + m<B. What theorem justifies this?

In triangle ABC, AB = AC. A proof states that angle B is congruent to angle C. Which theorem justifies the statement?

After proving triangle ABC ≅ triangle DEF, a proof states BC ≅ EF. Which reason justifies that corresponding side statement?

In a right triangle, the legs are 7 cm and 24 cm and the hypotenuse is c. The proof writes c^2 = 7^2 + 24^2. What theorem justifies it?