G&M - 11 Angle relationships formed by two non-parallel lines, or parallel lines intersected by a transversal: When two non-parallel lines or two parallel lines are intersected by a transversal a number of angle relationships are formed.
Example 11.1 – Parallel and non-parallel lines cut by a transversal:
Example 11.2 – Some angle relationships formed by parallel and non-parallel lines being cut by a transversal:
Example 11.3 – Uses properties of angle relationships formed by two lines cut by a transversal to solve a problem:
Sam said that he could determine the measure of every angle in Figures A and B without actually measuring the angles if he knew just one of the angles in each of the figures.
Is Sam correct? Explain why or why not using an example.
Answer: Sam is incorrect. Given the measure of one angle in Figure A all the angles can be determined. However, because the lines being cut by the transversal are not parallel in Figure B, it is not possible to determine the measures of the corresponding angles in Figure B.
Figure A: For example, if the measure of angle 1 is 120°, then the measure of angle 4 is 120° because the measure of vertical angles is the same. Angles 1 and 2 form a linear pair. Therefore, the measure of 2 is 60° (180° – 120° = 60°). Angles 2 and 3 are vertical angles and, therefore, the measures of 3 is 60°. Because alternate interior and alternate exterior angles are congruent when two parallel lines are cut by a transversal, the measure of angle 5 is 120°, angle 6 is 60°, angle 7 is 60°, and angle 8 is 120°.