Question

identify the property that justifies each statement.

1. ( a + b = a + b )
2. if ( angle rst cong angle abc ), then ( angle abc cong angle rst ).
3. ( 2x = 9 ), and ( y = 9 ). so ( 2x = y ).

Explanation:

• For the statement \(a + b=a + b\), the reflexive property of equality states that any quantity is equal to itself. Here, \(a + b\) is equal to itself.
• For the statement "If \(\angle RST\cong\angle ABC\), then \(\angle ABC\cong\angle RST\)", the symmetric property of congruence (which is similar to the symmetric property of equality for congruent angles) says that if one angle is congruent to another, then the second angle is congruent to the first.
• For the statement "If \(2x = 9\) and \(y=9\), then \(2x=y\)", the transitive property of equality states that if \(a = b\) and \(b = c\), then \(a = c\). Here \(a = 2x\), \(b = 9\), and \(c=y\).

Answer:

1. Reflexive Property of Equality
2. Symmetric Property of Congruence
3. Transitive Property of Equality