Question

topic 4: proof
write the letter of the property, definition, or postulate that justifies each statement.

1. if ∠abc ≅ ∠cbd, then ∠cbd ≅ ∠abc
2. if vw + wy = zy, and vw + wy = xz, then xz = zy
3. if s is between r and t, then rs + st = rt
4. if jk + kl = mn + kl, then jk = mn
5. if m∠a = m∠c, and m∠c = m∠d, then m∠a = m∠d
6. if pq = qt, then pq + rs = qt + rs
7. m∠def = m∠def
8. if ½xz = xy, then xz = 2xy
9. if m∠lmn = m∠mnp, then ∠lmn ≅ ∠mnp

a. addition property of equality
b. subtraction property of equality
c. multiplication property of equality
d. division property of equality
e. substitution property
f. reflexive property (of = or ≅)
g. symmetric property (of = or ≅)
h. transitive property (of = or ≅)
i. definition of congruence
j. definition of midpoint
k. segment addition postulate
l. angle addition postulate
© gina wilson (all things algebra), 2014

Explanation:

Question 29

Step1: Identify the property

The statement shows that if \( \angle ABC \cong \angle CBD \), then \( \angle CBD \cong \angle ABC \). This is the Symmetric Property of congruence, which states that if \( a \cong b \), then \( b \cong a \).

Step2: Match with the option

Looking at the options, option G is the Symmetric Property (of \( = \) or \( \cong \)).

Step1: Identify the property

We have two equal expressions (\( VW + WY = ZY \) and \( VW + WY = XZ \)) and we conclude \( XZ = ZY \) by substituting one equal expression for the other. This is the Substitution Property.

Step2: Match with the option

Option E is the Substitution Property.

Step1: Identify the property

The statement says if \( S \) is between \( R \) and \( T \), then \( RS + ST = RT \). This is the Segment Addition Postulate, which states that if a point is between two other points on a segment, the sum of the two smaller segments equals the larger segment.

Step2: Match with the option

Option K is the Segment Addition Postulate.

Answer:

G. Symmetric Property (of = or ≅)

Question 30