Question

ch. 2.5 & 2.6 - postulates & algebraic proofs - practice
match the given statements with the correct property or definition.
possible points: 33.33
if m is the midpoint 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 midpoint
:: transitive property :: definition of complementary angles :: addition postulate

Explanation:

1. The statement "If M is the mid - point of $\overline{RT}$, then $\overline{RM}\cong\overline{MT}$" follows the Definition of Midpoint as a mid - point divides a line segment into two congruent segments.
2. "If $GH = PR$, then $PR=GH$" is an example of 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 based on the Addition Postulate which allows adding the same quantity to both sides of an equation.
4. "If $\overline{RT}\cong\overline{SW}$ and $\overline{SW}\cong\overline{OP}$, then $\overline{RT}\cong\overline{OP}$" follows the Transitive Property which says 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 for angles, where equal measures imply congruence.
6. "If two lines are perpendicular, then they form complementary angles" is incorrect. Perpendicular lines form right angles (90 degrees). Complementary angles add up to 90 degrees, but this is not the correct property for perpendicular lines.
7. "If two angles are a linear pair, then they are supplementary" is the Definition of Supplementary Angles as linear pairs of angles add up to 180 degrees.

Answer:

1. Definition of Midpoint
2. Symmetric Property
3. Addition Postulate
4. Transitive Property
5. Definition of Congruence
6. None of the given (as the statement is wrong about perpendicular lines forming complementary angles)
7. Definition of Supplementary Angles