Download 2.6 Lines and Angles

2.6 Lines and Angles
Warm Up
Identify each of the following terms or objects.
1. points that lie in the same plane
Coplanar points
2. two angles whose sum is 180°
Supplementary angles
3. the intersection of two distinct intersecting lines
A point
4. a pair of adjacent angles whose non-common sides are
opposite rays
Linear pair of angles
2.6 Lines and Angles
Objectives
Prove and use theorems about the angles
formed by parallel lines and a transversal.
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
Corresponding Angles Postulate
∥ 𝒍𝒊𝒏𝒆𝒔 𝒄𝒖𝒕 𝒃𝒚 𝒕𝒓𝒂𝒏𝒔.
𝐂𝐀 ≅
𝑝∥𝑞
Conclusion
∠1 ≅ ∠3
∠2 ≅ ∠4
∠5 ≅ ∠7
∠6 ≅ ∠8
Alternate interior Angles Theorem
∥ 𝒍𝒊𝒏𝒆𝒔 𝒄𝒖𝒕 𝒃𝒚 𝒕𝒓𝒂𝒏𝒔.
𝐀𝐈𝐀 ≅
∠2 ≅ ∠7
∠3 ≅ ∠6
Alternate Exterior Angles Theorem
∥ 𝒍𝒊𝒏𝒆𝒔 𝒄𝒖𝒕 𝒃𝒚 𝒕𝒓𝒂𝒏𝒔.
𝐀𝐄𝐀 ≅
∠1 ≅ ∠8
∠4 ≅ ∠5
Same-Side Interior Angles Theorem
∥ 𝒍𝒊𝒏𝒆𝒔 𝒄𝒖𝒕 𝒃𝒚 𝒕𝒓𝒂𝒏𝒔.
𝐒𝐒𝐈𝐀 𝒔𝒖𝒑𝒑.
𝑚∠2 + 𝑚∠3 = 180°
𝑚∠6 + 𝑚∠7 = 180°
When two parallel lines are cut by a transversal, any pair of angles
congruent
supplementary
will either be __________________
or _____________________.
Example 2:
Find mQRS.
Example 3:
Find each angle measure.
A. mDCE
B. mECF
Example 4:
Find mABD.
Example 5:
Find mABD.
Finished 1st amd 3rd hour
Example 6:
Find the measure of all numbered angles in the diagram.
1=
2=
3=
4=
5=
6=
7=
8=
9=
10 =
35°
Example 7:
Proof of the Alternate Exterior Angles Theorem
Given: 𝑙 ∥ 𝑚
Prove: ∠1 ≅ ∠3
2
3
Statements
1. 𝑙 ∥ 𝑚
2. ∠1 ≅ ∠2
3. ∠2 ≅ ∠3
4. ∠1 ≅ ∠3
Reasons
1. Given
2. Corresp. ∠ Post
3. Vert. ∠ Thm.
4. Trans. Prop ≅
Example 8:
𝑚∠2 + 𝑚∠3 = 180°
Corresp. ∠ Post.
𝑚∠1 = 𝑚∠2
𝑚∠1 + 𝑚∠3 = 180°
Subst. Prop.