Question

State the property that justifies each statement.

If angle 1 is congruent to angle 2 and angle 2 is congruent with angle 3, then angle 1 is congruent with angle 3.

a. Transitive Property of Congruence
b. Reflexive Property of Congruence
c. Symmetric Property of Congruence
d. Substitution Property

If angle ABC is congruent to angle DEF, then angle DEF is congruent to ABC.

a. Transitive Property of Congruence
b. Reflexive Property of Congruence
c. Symmetric Property of Congruence
d. Substitution Property

If 2x + y = 5 and x = y, then 2x + x = 5.

a. Addition Property of Equality
b. Multiplication Property of Equality
c. Subtraction Property of Equality
d. Division Property of Equality

If the measure of angle A = 15, then 3 times the measure of angle A = 45 degrees.

a. Addition Property of Equality
b. Multiplication Property of Equality
c. Subtraction Property of Equality
d. Division Property of Equality

Answer 1

The Transitive Property of Congruence, Symmetric Property of Congruence, Substitution Property, and Multiplication Property of Equality are the properties that justify the given statements in mathematical reasoning.

Step-by-step explanation:

The properties that justify the given mathematical statements are:

1. If angle 1 is congruent to angle 2 and angle 2 is congruent with angle 3, then angle 1 is congruent with angle 3. The property that justifies this statement is the Transitive Property of Congruence.
2. If angle ABC is congruent to angle DEF, then angle DEF is congruent to ABC. This statement is justified by the Symmetric Property of Congruence.
3. If 2x + y = 5 and x = y, then 2x + x = 5. The property used here is the Substitution Property, as x is substituted for y in the equation.
4. If the measure of angle A = 15, then 3 times the measure of angle A = 45 degrees. This uses the Multiplication Property of Equality because you are multiplying both sides of an equation by the same number.