#### Math - 2019-20

# G.2 - Transversal Angles

G.2The student willusethe relationships between angles formed by two lines intersected by a transversal toa)

provetwo or more lines are parallel;b)

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

*Adopted: 2016*

### 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

· 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.2a_{1} **Prove**
two or more lines are parallel given angle measurements expressed numerically
or algebraically.

· G.2a_{2} **Prove**
two lines are parallel using deductive proofs given relationships between and
among angles.

· G.2b_{1} **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.2b_{2} **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*