Complete the two-column proof.
Given:<2=<4, m<2= 110 degrees
Prove:m∠3 = 70º
<2=<4, m<2= 110 degrees Given
m∠2 = m∠4 Definition of congruent angles
m∠4 = 110º b. ________
∠3 and ∠4 are a linear pair Definition of a linear pair (shown in diagram)
∠3 and ∠4 are supplementary Linear Pair postulate
m∠3 + m∠4 = 180º
m∠3 = 70º d. ________
damn 6 years later, and still no response
damn 6 years later, and the curriculum still hasn't changed
A. substitution property of equality, b. supplementary angles, and c. subtraction property of equality
(this might differ for everyone. i got full credit for this answer, but i cannot say for everyone)
Question is still the same this year too
its D. triangle angle sum theorem
Given:<2=<4, m<2= 110 degrees
Prove:m∠3 = 70º
<2=<4, m<2= 110 degrees Given
m∠2 = m∠4 Definition of congruent angles
m∠4 = 110º b. Get out your calculator and start adding.
∠3 and ∠4 are a linear pair Definition of a linear pair (shown in diagram)
∠3 and ∠4 are supplementary Linear Pair postulate
m∠3 + m∠4 = 180º
m∠3 = 70º d. It's basic math, just subtract 110 from 180!
To complete the two-column proof, you need to provide the missing statements and reasons.
Here is the completed proof:
Given: <2=<4, m<2 = 110 degrees
Prove: m∠3 = 70º
Statements Reasons
----------------------------------------------------------
<2=<4, m<2 = 110 degrees Given
m∠2 = m∠4 Definition of congruent angles
m∠4 = 110º Given (from statement 2)
∠3 and ∠4 are a linear pair Definition of a linear pair (shown in diagram)
∠3 and ∠4 are supplementary Linear Pair postulate
m∠3 + m∠4 = 180º Definition of supplementary angles
m∠3 + 110º = 180º Substitution (from statements 4 and 5)
m∠3 = 70º Subtraction property of equality
So, the missing statements are:
b. m∠4 = 110º (Given)
d. m∠3 = 70º (Subtraction property of equality)