Originally Posted by

**BobGnarley** Here are a few problems. Give me the reasons. This will make the difference to wether I pass the class for the six weeks. I am a few points away from passing.

1. Given: Q is the midpoint of PR, R is the midpoint of QS

Prove: PR = QS

*Statements*

a. Q is the midpoint of PR GIVEN

b. PQ = QR DEFINITION OF MIDPOINT

c. R is the midpoint of QS GIVEN

d. QR = RS DEFINITION OF MIDPOINT

e. PQ+QR=QR+RS ADDITION

f. PQ+QR=PR, QR+RS=QS SEGMENT ADDITION POSTULATE

g. PR=QS SUBSTITUTION (e) AND (f).

2. Given: line segment AB =~ line segment DE, line segment BC =~ to line segment EF

Prove: line segment AC =~ line segment DF

It is 2 parallel lines. Points ABC are on one line and DEF are on the other.

I'M PRETTY SURE YOU STATED THIS ONE INCORRECTLY, BUT I THINK I SEE THE PICTURE. YOU HAVE TWO PARALLEL LINES CUT BY TWO TRANSVERSALS, THUS CUTTING OFF CONGRUENT SEGMENTS ON THE PARALLEL LINES.

*Statements*

a. line segment AB =~ line segment DE GIVEN

b. AB = DE DEFINITION OF CONGRUENT SEGMENTS

c. line segment BC =~ line segment EF GIVEN

d. BC = EF DEFINITION OF CONGRUENT SEGMENTS

e. AB+BC=DE+EF ADDITION

f. AB+BC=AC, DE+EF=DF SEGMENT ADDITION POSTULATE

g. AC = DF SUBSTITUTION (e), (f)

h. line segment AC =~ line segment DF DEFINITION OF CONGRUENT SEGMENTS

3. Given AB perpendicular to BC, andgle 1 and angle 3 are complementary

Prove angle 2 =~ angle 3

IN THIS ONE, YOU HAVE TWO ADJACENT ANGLES 1 AND 2 THAT MAKE UP RIGHT ANGLE ABC. YOU HAVE A THIRD INDEPENDENT ANGLE 3 THAT IS COMPLEMENTARY TO ANGLE 2.

*Statements*

a. AB perpendicular to BC GIVEN

b. angle ABC = 90 PERPENDICULAR LINES MEET TO FORM RIGHT ANGLES

c. angle 1 + angle 2 = angle ABC ANGLE ADDITION POSTULATE

d. angle 1 and andgle 2 form a right angle SUBSTITUTION (b), (c)

e. angle 1 and angle 2 are complementary DEFINITION OF COMPLEMENTARY ANGLES

f. angle 1 and angle 3 are complementary GIVEN

g. angle 2 =~ angle 3 TWO ANGLES COMPLEMENTARY TO THE SAME ANGLE ARE CONGRUENT