Question

match the given statements with the correct property or definition.
if m is the mid - point of $overline{rt}$, then $overline{rm}congoverline{mt}$
if $gh = pr$, then $pr = gh$
if $dc = kl$, then $dc+xy = kl + xy$
if $overline{rt}congoverline{sw}$ and $overline{sw}congoverline{op}$, then $overline{rt}congoverline{op}$
if $mangle t=mangle z$, then $angle tcongangle z$
if two lines are perpendicular, then they form complementary angles.
if two angles are a linear pair, then they are supplementary.
:: definition of congruence :: symmetric property :: definition of supplementary angles :: definition of mid - point :: transitive property :: definition of complementary angles :: addition postulate

Explanation:

1. If M is the mid - point of $\overline{RT}$, then $\overline{RM}\cong\overline{MT}$ is the Definition of Midpoint as a mid - point divides a line segment into two congruent segments.
2. If $GH = PR$, then $PR=GH$ is the Symmetric Property which states that if $a = b$, then $b = a$ for real numbers or congruent geometric figures.
3. If $DC = KL$, then $DC+XY=KL + XY$ is the Addition Postulate which says that if equal quantities are added to equal quantities, the sums are equal.
4. If $\overline{RT}\cong\overline{SW}$ and $\overline{SW}\cong\overline{OP}$, then $\overline{RT}\cong\overline{OP}$ is the Transitive Property which states that if $a\cong b$ and $b\cong c$, then $a\cong c$.
5. If $m\angle T=m\angle Z$, then $\angle T\cong\angle Z$ is the Definition of Congruence as two angles are congruent if they have the same measure.
6. If two lines are perpendicular, then they form complementary angles is incorrect as perpendicular lines form right angles (90 degrees). But if we consider the concept related to the options, it is related to the Definition of Complementary Angles (two angles whose sum is 90 degrees).
7. If two angles are a linear pair, then they are supplementary is the Definition of Supplementary Angles as the sum of angles in a linear pair is 180 degrees.

Answer:

1. Definition of Midpoint
2. Symmetric Property
3. Addition Postulate
4. Transitive Property
5. Definition of Congruence
6. Definition of Complementary Angles
7. Definition of Supplementary Angles