Question

given: ( mangle a + mangle b = mangle b + mangle c )
prove: ( mangle c = mangle a )
write a paragraph proof to prove the statement.
to prove ( mangle c = mangle a ) given ( mangle a + mangle b = mangle b + mangle c ), we apply the subtraction property of equality, subtract ( mangle b ) from both sides of the equation.
sample response: we are given that the sum of the measures of angles a and b is equal to the sum of the measures of angles b and c. the measure of angle b is equal to itself by the reflexive property, so you can subtract that measure from both sides of the equation. now the measure of angle a equals the measure of angle c. by the symmetric property, this means the measure of angle c equals the measure of angle a.
what did you include in your response? check all that apply.
☐ reflexive property
☐ subtract
☐ symmetric property

Explanation:

1. The sample response mentions the measure of angle B is equal to itself (reflexive property).
2. It says to subtract the measure of angle B from both sides (subtract is included).
3. It then uses the symmetric property to state \( m\angle C = m\angle A \) from \( m\angle A = m\angle C \). So all three options are included.

Answer:

• reflexive property
• subtract
• symmetric property