DIAGRAMS WOULD'VE BEEN NICE. And by the way, I'm not flaming by using all caps. This is just for contrast. So relax.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
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.
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.
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