Question

name that segment postulate
type answers in canvas.
1 if ( pq = pq ), then ( overline{pq}congoverline{pq} )
2 if ( k ) is between ( j ) and ( l ), then ( jk + kl = jl )
2 ( overline{ef}congoverline{ef} )
4 if ( rs = tu ), then ( rs + xt = tu + xt )
5 if ( ab = de ), then ( de = ab )
6 if ( t ) is the midpoint of ( overline{xz} ), then ( xt = yz )
1 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 midpoint of ( overline{ln} )
11 if ( overline{uv}congoverline{uv} ), then ( ut = uv )
12 if ( cd + de = ce ), then ( cd = ce - de )
property bank
properties of equality:
addition property
subtraction property
multiplication property
division property
distributive property
substitution property
reflexive property
symmetric property
transitive property
properties of congruence:
reflexive property
symmetric property
transitive property
definitions:
definition of congruence
definition of midpoint
postulates:
segment addition postulate

Explanation:

1. Segment Addition Postulate: If \(K\) is between \(J\) and \(L\), then \(JK + KL=JL\) by the definition of the Segment Addition Postulate which states that if a point lies between two other points on a line segment, the sum of the lengths of the two smaller segments is equal to the length of the larger segment.
2. Reflexive Property of Congruence: \(\overline{EF}\cong\overline{EF}\) because the reflexive property of congruence states that any geometric figure is congruent to itself.
3. Addition Property of Equality: If \(RS = TU\), then \(RS+XT = TU + XT\) as the addition property of equality allows us to add the same quantity to both sides of an equation.
4. Symmetric Property of Equality: If \(AB = DE\), then \(DE = AB\) since the symmetric property of equality states that if \(a = b\), then \(b=a\).
5. Definition of Midpoint: If \(T\) is the midpoint of \(\overline{XZ}\), then \(XT = YZ\) (assuming a typo and it should be \(XT= TZ\)) because the midpoint of a segment divides it into two equal - length parts.
6. Transitive Property of Congruence: If \(\overline{FG}\cong\overline{HI}\) and \(\overline{HI}\cong\overline{JK}\), then \(\overline{FG}\cong\overline{JK}\) by the transitive property of congruence (\(a\cong b\) and \(b\cong c\) implies \(a\cong c\)).
7. Subtraction Property of Equality: If \(AB + CD=EF + CD\), then \(AB = EF\) as we can subtract \(CD\) from both sides of the equation.
8. Substitution Property of Equality: If \(PQ + RS=TV\) and \(RS = WX\), then \(PQ + WX=TV\) because we substitute \(WX\) for \(RS\) in the first equation.
9. Definition of Midpoint: If \(LP = PN\) and \(L\), \(P\), and \(N\) are collinear, then \(P\) is the midpoint of \(\overline{LN}\) as the midpoint is the point on a line segment that divides it into two equal - length parts.
10. Definition of Congruence: If \(\overline{UV}\cong\overline{UV}\), then \(UT = UV\) (assuming a typo and it should be \(UV = UV\) which is the reflexive property of congruence, but if we consider the length, the definition of congruent segments means their lengths are equal).
11. Subtraction Property of Equality: If \(CD + DE=CE\), then \(CD=CE - DE\) as we can subtract \(DE\) from both sides of the equation.

Answer:

1. Definition of Congruence
2. Segment Addition Postulate
3. Reflexive Property of Congruence
4. Addition Property of Equality
5. Symmetric Property of Equality
6. Definition of Midpoint
7. Transitive Property of Congruence
8. Subtraction Property of Equality
9. Substitution Property of Equality
10. Definition of Midpoint
11. Definition of Congruence
12. Subtraction Property of Equality