Parallel Line Proofs PARTI. USE THE DIAGRAM TO COMPLETE THE PROOFS
A) Given: m 1 = (2x - 135)
m2 = (x - 30)
Prove: x = 105
B) Given: mZ1 = (10x)
mZ3 = (9x + 28)
Prove: m23 = 100
Statements
Justifications
Statements
Justifications
1.
1.
1.
1.
2.
2. Corr. Post.
2.
2. Linear Pair Post
3. 2x - 135 = x - 30
3
3.
3. Substitution
4.
4. Subtraction Prop
4.
4. Combine Like Terms
5.
5.
5. 19x = 152
S
6.
6. Division
7. m3 = 100°
7.
C) Given: The diagram
Prove: m2 + m23 = 180°
Statements
Justifications
1. mZ1 + m23 = 180°
1.
2. m1 = m22
3. m2 + m23 = 180°
3

Data from 2005 for various age groups show that for each $100 increase in the median weekly income for whites, the median weekly income of blacks increases by $105. also, for workers of ages 25 to 54 the median weekly income for whites was $676 and for blacks was $527. (a) let w represent the median weekly income for whites and b the median weekly income for blacks, and write the equation of the line that gives b as a linear function of w. b = (b) when the median weekly income for whites is $760, what does the equation in (a) predict for the median weekly income for blacks?