Question

in the figure shown, lines f and g are parallel. select the angle that is congruent to angle 1.
a. angle 2
b. angle 6
c. angle 7
d. angle 8
describe a rigid transformation that could be used to show that corresponding angles are congruent.

Explanation:

Step1: Recall the property of vertical angles

Vertical angles are congruent. Angle 1 and Angle 3 are vertical angles, Angle 2 and Angle 4 are vertical angles, Angle 5 and Angle 7 are vertical angles, Angle 6 and Angle 8 are vertical angles.

Step2: Recall the property of corresponding angles

Since lines \(f\) and \(g\) are parallel, corresponding angles are congruent. Angle 1 and Angle 5 are corresponding angles, Angle 2 and Angle 6 are corresponding angles, Angle 3 and Angle 7 are corresponding angles, Angle 4 and Angle 8 are corresponding angles.

Step3: Find the angle congruent to Angle 1

By the property of vertical angles, Angle 1\(\cong\)Angle 3. By the property of corresponding angles (because \(f\parallel g\)), Angle 1\(\cong\)Angle 5. By the property of vertical angles again, Angle 5\(\cong\)Angle 7. So Angle 1\(\cong\)Angle 7.

Answer:

c. Angle 7