#### Math - 2017-18

# 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.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.

**Bloom's Level:** Evaluate

*Adopted: 2009*

### 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.2a_{1} **Use** algebraic and coordinate methods as
well as deductive proofs to **verify**
whether 2 lines are parallel.

· 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 2 parallel
lines and a transversal including corresponding angles, alternate interior
angles, alternate exterior angles, and same-side (consecutive) interior 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.2c_{1} **Solve** real-world problems involving
intersecting and parallel lines in a plane.

· 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: Oct 27, 2017*