Question

When GF and CD are both perpendicular to AB, what relationship exists between GF and CD?

a) They intersect at a right angle
b) They are parallel to each other
c) They form obtuse angles
d) They are not related

When CD is not perpendicular to AB, what type of angles can be formed by AB as a transversal line with GF and CD?
a) Right angles
b) Vertical angles
c) Supplementary angles
d) Corresponding angles

Answer 1

GF and CD are parallel when both are perpendicular to AB. When CD is not perpendicular, AB with GF and CD can form supplementary or corresponding angles, depending on the angles' positions and CD's direction.

Step-by-step explanation:

When GF and CD are both perpendicular to AB, they are parallel to each other, since two lines that are perpendicular to the same line are parallel. Therefore, the relationship that exists between GF and CD is that they are parallel.

When CD is not perpendicular to AB, the angles formed by AB as a transversal line with GF and CD can be supplementary if GF remains perpendicular to AB or corresponding if the angles lie in the same position at each intersection. This is determined by the relative direction and angle of CD with respect to AB and GF.