Question

practice! property of congruence, definition, or postulate.

1. if (pq = pq), then (overline{pq}congoverline{pq}).
2. if (k) is between (j) and (l), then (jk + kl=jl).
3. (overline{ef}congoverline{ef}).
4. if (rs = tu), then (rs+xy = tu + xy).
5. if (ab = de), then (de = ab).
6. if (y) is the mid - point of (overline{xz}), then (xy = yz).
7. if (overline{fg}congoverline{hi}) and (overline{hi}congoverline{jk}), then (overline{fg}congoverline{jk}).
8. if (ab + cd=ef + cd), then (ab = ef).
9. if (pq + rs = tv) and (rs = wx), then (pq+wx = tv).
10. if (lp = pn) and (l), (p), and (n) are collinear, then (p) is the mid - point of (overline{ln}).
11. if (overline{ut}congoverline{uv}), then (ut = uv).
12. if (cd + de = ce), then (cd = ce - de).

Explanation:

Step1: Identify reflexive property

The reflexive property states that a quantity is equal to itself. For 1. If $PQ = PQ$, then $\overline{PQ}\cong\overline{PQ}$ and 3. $\overline{EF}\cong\overline{EF}$, these are examples of the reflexive property of congruence.

Step2: Identify segment - addition postulate

The segment - addition postulate says that if a point $K$ is between points $J$ and $L$, then $JK + KL=JL$. So 2. is an example of the segment - addition postulate.

Step3: Identify addition property of equality

The addition property of equality states that if $a = b$, then $a + c=b + c$. For 4. If $RS = TU$, then $RS+XY = TU + XY$, this is the addition property of equality.

Step4: Identify symmetric property of equality

The symmetric property of equality states that if $a = b$, then $b = a$. So for 5. If $AB = DE$, then $DE = AB$, this is the symmetric property of equality.

Step5: Identify mid - point definition

The mid - point of a segment divides the segment into two equal parts. For 6. If $Y$ is the mid - point of $\overline{XZ}$, then $XY = YZ$, this is the definition of a mid - point.

Step6: Identify transitive property of congruence

The transitive property of congruence states that if $a\cong b$ and $b\cong c$, then $a\cong c$. For 7. If $\overline{FG}\cong\overline{HI}$ and $\overline{HI}\cong\overline{JK}$, then $\overline{FG}\cong\overline{JK}$, this is the transitive property of congruence.

Step7: Identify subtraction property of equality

The subtraction property of equality states that if $a + c=b + c$, then $a = b$. For 8. If $AB + CD=EF + CD$, then $AB = EF$, this is the subtraction property of equality.

Step8: Identify substitution property of equality

The substitution property of equality states that if $a = b$, then $a$ can be substituted for $b$ in any equation. For 9. If $PQ + RS=TV$ and $RS = WX$, then $PQ+WX = TV$, this is the substitution property of equality.

Step9: Identify mid - point definition (converse)

If $LP = PN$ and $L$, $P$, and $N$ are collinear, then $P$ is the mid - point of $\overline{LN}$, this is the converse of the mid - point definition.

Step10: Identify symmetric property of congruence

If $\overline{UT}\cong\overline{UV}$, then $\overline{UV}\cong\overline{UT}$ (a re - statement of congruence with order reversed), this is the symmetric property of congruence for 11.

Step11: Identify subtraction property of equality

If $CD + DE=CE$, then $CD=CE - DE$ by the subtraction property of equality for 12.

Answer:

1. Reflexive property of congruence
2. Segment - addition postulate
3. Reflexive property of congruence
4. Addition property of equality
5. Symmetric property of equality
6. Definition of mid - point
7. Transitive property of congruence
8. Subtraction property of equality
9. Substitution property of equality
10. Definition of mid - point (converse)
11. Symmetric property of congruence
12. Subtraction property of equality