# G.2 - Transversal Angles

G.2  The student will use the relationships between angles formed by two lines intersected by a transversal to

a)  prove two or more lines are parallel;

b)  solve problems, including practical problems, involving angles formed when parallel lines are intersected by a transversal.

### BIG IDEAS

• I can make a double bank shot in an air hockey game, build a handrail on a downhill slope, determine the angle of the sun based on colors in a rainbow, and correctly paint the lines in a parking lot.
• I will determine angle measurements and relationships, and by using patterns and the positions of angles be able to confirm parallel lines.

### UNDERSTANDING THE STANDARD

2016 VDOE Curriculum Framework - G.2 Understanding

·  Deductive or inductive reasoning is used in mathematical proofs.  In this course, deductive reasoning and logic are used in direct proofs. Direct proofs are presented in different formats (typically two-column or paragraph) and employ definitions, postulates, theorems, and algebraic justifications including coordinate methods.

·  Parallel lines intersected by a transversal form angles with specific relationships.

·  Some angle relationships may be used when proving two lines intersected by a transversal are parallel.

·  If two parallel lines are intersected by a transversal, then:

­  corresponding angles are congruent;

­  alternate interior angles are congruent;

­  alternate exterior angles are congruent;

­  same-side (consecutive) interior angles are supplementary; and

­  same-side (consecutive) exterior angles are supplementary.

·  Deductive proofs can be used to show that two or more lines are parallel.

·  The construction of the line parallel to a given line through a point not on the line can be justified using the angle relationships formed when two lines are intersected by a transversal.

### ESSENTIALS

The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

·  G.2a1  Prove two or more lines are parallel given angle measurements expressed numerically or algebraically.

·  G.2a2  Prove two lines are parallel using deductive proofs given relationships between and among angles.

·  G.2b1  Solve problems by using the relationships between pairs of angles formed by the intersection of two parallel lines and a transversal including corresponding angles, alternate interior angles, alternate exterior angles, same-side (consecutive) interior angles, and same-side (consecutive) exterior angles.

·  G.2b2  Solve problems, including practical problems, involving intersecting and parallel lines.

### KEY VOCABULARY

lines, transversal, parallel, angles, skew lines, parallelism, algebraic method, coordinate method, deductive proof, intersection, corresponding angles, alternate interior angles, alternate exterior angles, consecutive/same-side interior angles, plane, angle relationships, equidistant, Parallel Postulate

Updated: Jul 30, 2019