Question

Name the property that justifies each of the following statements

1) if m1=40 and m2=60 then m1+m2=100 (angle measures)
2) if CD+ON=PQ, then CD=PQ-ON

Answer 1

The additive property of equality justifies adding two angles' measures to get a sum, while the subtraction property of equality allows for the isolation of one term by subtracting the same value from both sides of an equation.

Step-by-step explanation:

The properties that justify each statement are as follows:

1. For the statement if m1=40 and m2=60 then m1+m2=100 (angle measures), the property used is the additive property of equality. This means that if two angles measure 40 degrees and 60 degrees, then the sum of their measures equals 100 degrees.
2. For the statement if CD+ON=PQ, then CD=PQ-ON, the property that justifies this is the subtraction property of equality. This allows us to subtract the same value, ON, from both sides of the equation CD+ON=PQ to isolate CD, demonstrating that CD is equal to PQ minus ON.