Answer to Question #284653 in Geometry for sophia

Question

m is a straight line with a 1 on the right side.

n is a straight line with a number 3 & 2 in the middle but there’s a diagonal line that goes straight through both lines and the numbers 3 & 2 are in between that diagonal line.

Given: Line m is parallel to line n.

Prove: <1 is supplementary to <3

statement: reason:

S1. Line m is parallel to line n. R1. given

S2. <1 =~ <2 R2. ?

S3. m<1 =~ m<2. R3. ?

S4. <2 & <3 for a linear pair. R4. definition of linear pair

S5. <2 is supplementary to <3 R5. ?

S6. m<2 + m<3 = 180° R6. definition of supplementary

S7. ? R7. Substitution Property of Equality

S8. ? R8. Definition of supplementary

Answer 1

Prove: <1 is supplementary to <3-supplementary since both they add up to 180

S2. <1 =~ <2 R2. ?-they are parallel since they do not intersect or meet at any point

m<1 =~ m<2. R3. ?-they don't intersect anypoint

Linear pair-a pair of adjacent angles formed when two lines intersect.

<2 is supplementary to <3 R5. -supplementary as they add up to 180

Supplementary-angles add up to 180 degrees

Substitution Property of Equality-The substitution property of equality, one of the eight properties of equality, states that if x = y, then x can be substituted in for y in any equation, and y can be substituted for x in any equation.

Supplementary angles are the ones that add up to 180 degrees