Warm Up

Identify each of the following terms or objects.1. points that lie in the same plane

2. two angles whose sum is 180°

3. the intersection of two distinct intersecting lines

4. a pair of adjacent angles whose non-common sides are opposite rays

2.6 Lines and Angles

Coplanar points

Supplementary angles

A point

Linear pair of angles

ObjectivesProve and use theorems about the angles formed by parallel lines and a transversal.

2.6 Lines and Angles

Example 1:

Give an example of each angle pair.

A. corresponding angles

B. alternate interior angles

C. alternate exterior angles

D. same-side interior angles

Postulate or Theorem Hypothesis ConclusionCorresponding Angles Postulate

Alternate interior Angles Theorem

Alternate Exterior Angles Theorem

Same-Side Interior Angles Theorem

When two parallel lines are cut by a transversal, any pair of angles will either be __________________ or _____________________.congruent supplementary

Example 2:

Find mQRS.

Example 3:

Find each angle measure.

A. mDCE

B. mECF

Example 4:

Find mABD.

Example 5:

Find mABD.

Finished 1st amd 3rd hour

35°

Example 6:Find the measure of all numbered angles in the diagram.

1 =2 =3 =4 =5 =

6 =7 =8 =9 =10 =

23

Example 7:Proof of the Alternate Exterior Angles TheoremGiven: Prove:

Statements Reasons1. 1.2. 2.3. 3.4. 4.

𝑙 ∥𝑚∠1≅∠2∠2≅∠3∠1≅∠3

GivenCorresp. PostVert. Thm.Trans. Prop

Example 8:

𝑚∠2+𝑚∠3=180 °Corresp. Post.

𝑚∠1=𝑚∠2𝑚∠1+𝑚∠3=180 ° Subst. Prop.