m of angle 1 + m of angle 2 = 90 degrees m of angle 3 = 90 degrees  m of angle 1 + m of angle 2 = m of angle 3is this the substitution property or is this the transitive property? (m means measure)

Asked on by thi-dallas

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embizze | High School Teacher | (Level 2) Educator Emeritus

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(1) `m/_1+m/_2=90^@` Given

(2) `m/_3=90^@`            Given

(3) `m/_1+m/_2=m/_3`   ?

(a)The transitive property of equality: `a=b,b=c ==>a=c`

Thus you could use the transitive property if you use the symmetric property of equality `(a=b ==> b=a)` on the equation in step 2:

`m/_1+m/_2=90^@,90^@=m/_3 ==>m/_1+m/_2=m/_3`

(b) The substitution property of equality allows you to substitute equal quantities. Then since `m/_1+m/_2=90^@` and `m/_3=90^@` we can substitute for `90^@` to get `m/_1+m/_2=m/_3`

As stated, I would use the substitution property of equality since you would not have to introduce another step. (As a teacher I would accept either answer, but some teachers might not)

** Note that while you can use substitution anytime you can use the transitive property (you might need to use the substitution property multiple times), it is not the case that you can use the transitive property in place of substitution at all times.

For example if angle 1 is supplementay to angle 2, and angle 2 is congruent to angle 3, then angle 1 is supplementary to angle 3 by substitution-- the transitive property cannot be used here.**

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