Geometry Notes2.2A

Solving Problems Applying Angle Properties of LinesLG.1.G.5 Explore, with and without appropriate technology, the relationship between angles formed by two lines cut by a transversal to justify when lines are parallelM.3.G.5 Identify and apply properties of and theorems about parallel and perpendicular lines to prove other theorems and perform basic Euclidean constructions

 

Review

When two parallel lines are cut by a transversal, what angles are congruent?

•Alternate interior angles, alternate exterior angles, and corresponding angles

When two parallel lines are cut by a transversal, what angles are supplementary?

•Same side interior angles

Example

•Given that a ll b, solve for x.1. Classify the angles (may have to transfer one

vertically)

2. Determine their relationship (either = 180 or = each other)

3. Set up an equation 4. Solve for x.

(10x + 45)

(19x) a

b

c

Now You Try… •Use the same steps as above to solve this

problem. Given that k ll l, solve for x

(2x - 15)

(x + 150)

k

l

p

Example

•Given that c ll d and l t, solve for x.

t

l

c

d

Now You Try…

(9x-1)۫ 12x۫

27x۫

a bc

d