# G.2 and *G.2 - Transversal Angles

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

a)  determine whether two lines are parallel;

b)  verify the parallelism, using algebraic and coordinate methods as well as deductive proofs; and

c)  solve real-world problems involving angles formed when parallel lines are cut by a transversal.

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.

Bloom's Level:  Evaluate

### 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

• 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.
• The Parallel Postulate differentiates Euclidean from non-Euclidean geometries such as spherical geometry and hyperbolic geometry.

·  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

G.2a1  Use algebraic and coordinate methods as well as deductive proofs to verify whether 2 lines are parallel.

·  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 2 parallel lines and a transversal including corresponding angles, alternate interior angles, alternate exterior angles, and same-side (consecutive) interior 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.2c1  Solve real-world problems involving intersecting and parallel lines in a plane.

·  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: Oct 27, 2017